%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW390+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:02 AM UTC 2026
% Result : Theorem 200.62s 71.35s
% Output : Refutation 221.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 4726
% Syntax : Number of formulae : 9789 (3117 unt; 0 typ; 2 def)
% Number of atoms : 25854 (9333 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 286258 (2689 ~; 858 |;2334 &;267606 @)
% ( 804 <=>;11967 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 427 ( 424 usr; 51 con; 0-6 aty)
% Number of variables : 31181 ( 0 ^;30763 !; 416 ?;31181 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v_P_decl,type,
v_P: $i > $i > $o ).
thf(c_Hoare__Mirabelle_Ohoare__derivs_decl,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(t_a_decl,type,
t_a: $i ).
thf(v_G_decl,type,
v_G: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i ).
thf(tc_Hoare__Mirabelle_Otriple_decl,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_HOL_Obool_decl,type,
tc_HOL_Obool: $i ).
thf(class_Rings_Oring__1_decl,type,
class_Rings_Oring__1: $i > $o ).
thf(c_Int_Oring__1__class_Oof__int_decl,type,
c_Int_Oring__1__class_Oof__int: $i > $i ).
thf(c_Groups_Ominus__class_Ominus_decl,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(tc_Int_Oint_decl,type,
tc_Int_Oint: $i ).
thf(c_Groups_Oone__class_Oone_decl,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
thf(c_Groups_Ozero__class_Ozero_decl,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).
thf(c_Int_Onat_decl,type,
c_Int_Onat: $i ).
thf(c_Groups_Ouminus__class_Ouminus_decl,type,
c_Groups_Ouminus__class_Ouminus: $i > $i ).
thf(class_Rings_Olinordered__idom_decl,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(c_Groups_Otimes__class_Otimes_decl,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $i > $o ).
thf(c_Int_Onumber__class_Onumber__of_decl,type,
c_Int_Onumber__class_Onumber__of: $i > $i ).
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(c_Groups_Oplus__class_Oplus_decl,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(c_Fun_Oid_decl,type,
c_Fun_Oid: $i > $i ).
thf(class_Groups_Ocomm__monoid__mult_decl,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_decl,type,
c_Big__Operators_Ocomm__monoid__mult__class_Osetprod: $i > $i > $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i ).
thf(c_Int_OMin_decl,type,
c_Int_OMin: $i ).
thf(c_member_decl,type,
c_member: $i > $i ).
thf(c_Int_Oring__1__class_OInts_decl,type,
c_Int_Oring__1__class_OInts: $i > $i ).
thf(c_Big__Operators_Ocomm__monoid__add__class_Osetsum_decl,type,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum: $i > $i > $i ).
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_List_Orev_decl,type,
c_List_Orev: $i > $i ).
thf(c_List_Orotate_decl,type,
c_List_Orotate: $i > $i > $i ).
thf(c_Nat_Ocompow_decl,type,
c_Nat_Ocompow: $i > $i > $i ).
thf(c_List_Orotate1_decl,type,
c_List_Orotate1: $i > $i ).
thf(c_Product__Type_Oprod_Oprod__case_decl,type,
c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_HOL_OLet_decl,type,
c_HOL_OLet: $i > $i > $i ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_If_decl,type,
c_If: $i > $i ).
thf(c_fequal_decl,type,
c_fequal: $i ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i ).
thf(c_Divides_Odivmod__int_decl,type,
c_Divides_Odivmod__int: $i > $i > $i ).
thf(c_Int_OBit0_decl,type,
c_Int_OBit0: $i > $i ).
thf(c_Int_OBit1_decl,type,
c_Int_OBit1: $i > $i ).
thf(c_Int_OPls_decl,type,
c_Int_OPls: $i ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i ).
thf(c_Com_Ocom_OWhile_decl,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(c_Com_Ocom_OLocal_decl,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(c_Int_Osucc_decl,type,
c_Int_Osucc: $i > $i ).
thf(class_Rings_Osemiring__1_decl,type,
class_Rings_Osemiring__1: $i > $o ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i ).
thf(c_Finite__Set_Ocard_decl,type,
c_Finite__Set_Ocard: $i > $i ).
thf(c_List_Olist__all2_decl,type,
c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).
thf(c_List_Omap_decl,type,
c_List_Omap: $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(class_Rings_Ono__zero__divisors_decl,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(class_Groups_Omonoid__mult_decl,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(c_Wellfounded_Oaccp_decl,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_Nitpick_Onat__gcd__rel_decl,type,
c_Nitpick_Onat__gcd__rel: $i ).
thf(c_Product__Type_OPair_decl,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_Nitpick_Onat__gcd_decl,type,
c_Nitpick_Onat__gcd: $i > $i > $i ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_Product__Type_Oapsnd_decl,type,
c_Product__Type_Oapsnd: $i > $i > $i > $i > $i ).
thf(c_Divides_Odivmod__nat__rel_decl,type,
c_Divides_Odivmod__nat__rel: $i > $i > $i ).
thf(c_Divides_Odivmod__nat_decl,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(c_List_Oreplicate_decl,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(c_Com_Ocom_OCond_decl,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(class_Rings_Olinordered__semiring__1__strict_decl,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(class_Rings_Olinordered__semiring__1_decl,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_List_Olist__ex_decl,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(c_Product__Type_Omap__pair_decl,type,
c_Product__Type_Omap__pair: $i > $i > $i > $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_List_Ofilter_decl,type,
c_List_Ofilter: $i > $i > $i ).
thf(c_List_Olinorder__class_Osort__key_decl,type,
c_List_Olinorder__class_Osort__key: $i > $i > $i > $i > $i ).
thf(c_List_Onth_decl,type,
c_List_Onth: $i > $i ).
thf(c_Com_Ocom_OSemi_decl,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Divides_OnegDivAlg_decl,type,
c_Divides_OnegDivAlg: $i > $i > $i ).
thf(c_Divides_Oadjust_decl,type,
c_Divides_Oadjust: $i > $i ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i ).
thf(c_Divides_Opdivmod_decl,type,
c_Divides_Opdivmod: $i > $i > $i ).
thf(c_Divides_Odiv__class_Odiv_decl,type,
c_Divides_Odiv__class_Odiv: $i > $i ).
thf(c_Groups_Oabs__class_Oabs_decl,type,
c_Groups_Oabs__class_Oabs: $i > $i ).
thf(c_Random_Oselect__weight_decl,type,
c_Random_Oselect__weight: $i > $i > $i ).
thf(c_Product__Type_Oscomp_decl,type,
c_Product__Type_Oscomp: $i > $i > $i > $i > $i ).
thf(tc_Code__Numeral_Ocode__numeral_decl,type,
tc_Code__Numeral_Ocode__numeral: $i ).
thf(c_Random_Orange_decl,type,
c_Random_Orange: $i > $i ).
thf(c_List_Omonoid__add__class_Olistsum_decl,type,
c_List_Omonoid__add__class_Olistsum: $i > $i ).
thf(c_Product__Type_Ofst_decl,type,
c_Product__Type_Ofst: $i > $i > $i ).
thf(c_Random_Opick_decl,type,
c_Random_Opick: $i > $i > $i ).
thf(class_Fields_Ofield__inverse__zero_decl,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(c_Rings_Oinverse__class_Odivide_decl,type,
c_Rings_Oinverse__class_Odivide: $i > $i ).
thf(class_Rings_Oring__1__no__zero__divisors_decl,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(c_List_Olinorder__class_Osorted_decl,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(c_Com_Ocom_OSKIP_decl,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_List_Oappend_decl,type,
c_List_Oappend: $i > $i ).
thf(c_Product__Type_Osnd_decl,type,
c_Product__Type_Osnd: $i > $i > $i ).
thf(c_List_Ofoldr_decl,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(c_List_Ofoldl_decl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i ).
thf(c_List_Odistinct_decl,type,
c_List_Odistinct: $i > $i ).
thf(class_Groups_Omonoid__add_decl,type,
class_Groups_Omonoid__add: $i > $o ).
thf(c_Random_Oselect_decl,type,
c_Random_Oselect: $i > $i > $i ).
thf(c_Wellfounded_Owf_decl,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(c_List_Olenlex_decl,type,
c_List_Olenlex: $i > $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i ).
thf(c_Divides_OnegateSnd_decl,type,
c_Divides_OnegateSnd: $i ).
thf(c_Divides_Odivmod__int__rel_decl,type,
c_Divides_Odivmod__int__rel: $i > $i > $i ).
thf(c_Fun_Ocomp_decl,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(c_Int_Opred_decl,type,
c_Int_Opred: $i > $i ).
thf(c_List_Olast_decl,type,
c_List_Olast: $i > $i > $i ).
thf(c_List_Ohd_decl,type,
c_List_Ohd: $i > $i ).
thf(class_Groups_Ocomm__monoid__add_decl,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(c_Code__Numeral_OSuc__code__numeral_decl,type,
c_Code__Numeral_OSuc__code__numeral: $i > $i ).
thf(c_Code__Numeral_Oof__nat_decl,type,
c_Code__Numeral_Oof__nat: $i ).
thf(c_Code__Numeral_Onat__of_decl,type,
c_Code__Numeral_Onat__of: $i ).
thf(c_List_Odrop_decl,type,
c_List_Odrop: $i > $i ).
thf(c_List_Otake_decl,type,
c_List_Otake: $i > $i ).
thf(c_Nat__Transfer_Otransfer__morphism_decl,type,
c_Nat__Transfer_Otransfer__morphism: $i > $i > $i > $i > $o ).
thf(c_Int_OAbs__Integ_decl,type,
c_Int_OAbs__Integ: $i ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i ).
thf(c_Int_Ointrel_decl,type,
c_Int_Ointrel: $i ).
thf(c_Divides_OnegDivAlg__rel_decl,type,
c_Divides_OnegDivAlg__rel: $i ).
thf(c_List_Olinorder__class_Osorted__list__of__set_decl,type,
c_List_Olinorder__class_Osorted__list__of__set: $i > $i > $i ).
thf(c_List_Oremdups_decl,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_List_Ozip_decl,type,
c_List_Ozip: $i > $i > $i ).
thf(c_List_Otl_decl,type,
c_List_Otl: $i > $i ).
thf(class_Fields_Ofield_decl,type,
class_Fields_Ofield: $i > $o ).
thf(c_List_Oconcat_decl,type,
c_List_Oconcat: $i > $i > $i ).
thf(c_Divides_OposDivAlg_decl,type,
c_Divides_OposDivAlg: $i > $i > $i ).
thf(c_List_Otranspose__rel_decl,type,
c_List_Otranspose__rel: $i > $i ).
thf(c_List_Otranspose_decl,type,
c_List_Otranspose: $i > $i > $i ).
thf(c_List_Olist__all_decl,type,
c_List_Olist__all: $i > $i > $i > $o ).
thf(c_List_Olist__update_decl,type,
c_List_Olist__update: $i > $i > $i ).
thf(class_Rings_Ocomm__ring_decl,type,
class_Rings_Ocomm__ring: $i > $o ).
thf(c_List_Olinorder__class_Oinsort__key_decl,type,
c_List_Olinorder__class_Oinsort__key: $i > $i > $i > $i ).
thf(c_Com_Ocom_Ocom__size_decl,type,
c_Com_Ocom_Ocom__size: $i > $i ).
thf(c_Groups_Osgn__class_Osgn_decl,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(c_HOL_OThe_decl,type,
c_HOL_OThe: $i > $i > $i ).
thf(c_Predicate_Opred__comp_decl,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i ).
thf(c_List_Osplice_decl,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(c_Relation_Orefl__on_decl,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_Relation_Oconverse_decl,type,
c_Relation_Oconverse: $i > $i > $i ).
thf(class_Lattices_Osemilattice__inf_decl,type,
class_Lattices_Osemilattice__inf: $i > $o ).
thf(c_Lattices_Osemilattice__inf__class_Oinf_decl,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i ).
thf(c_List_Olexn_decl,type,
c_List_Olexn: $i > $i > $i ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(c_Wellfounded_Olex__prod_decl,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_Set_OCollect_decl,type,
c_Set_OCollect: $i > $i ).
thf(c_fconj_decl,type,
c_fconj: $i ).
thf(c_Nat__Numeral_Oneg_decl,type,
c_Nat__Numeral_Oneg: $i ).
thf(c_Orderings_Oord__class_Omin_decl,type,
c_Orderings_Oord__class_Omin: $i > $i ).
thf(c_List_Oupt_decl,type,
c_List_Oupt: $i > $i > $i ).
thf(c_Relation_Ototal__on_decl,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(c_List_Oremove1_decl,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(class_Rings_Ocomm__semiring__1_decl,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(c_SetInterval_Oord__class_OlessThan_decl,type,
c_SetInterval_Oord__class_OlessThan: $i > $i ).
thf(c_Enum_On__lists_decl,type,
c_Enum_On__lists: $i > $i > $i > $i ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_decl,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(c_Predicate_ORangeP_decl,type,
c_Predicate_ORangeP: $i > $i > $i > $i ).
thf(c_List_Olinorder__class_Oinsort__insert__key_decl,type,
c_List_Olinorder__class_Oinsort__insert__key: $i > $i > $i > $i > $i > $i ).
thf(tc_Com_Ocom_decl,type,
tc_Com_Ocom: $i ).
thf(c_Divides_OposDivAlg__rel_decl,type,
c_Divides_OposDivAlg__rel: $i ).
thf(c_List_Osublist_decl,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(class_Lattices_Osemilattice__sup_decl,type,
class_Lattices_Osemilattice__sup: $i > $o ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(c_Wellfounded_Oacc_decl,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_List_Olistrel1_decl,type,
c_List_Olistrel1: $i > $i > $i ).
thf(class_Groups_Olinordered__ab__group__add_decl,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(c_Relation_Osym_decl,type,
c_Relation_Osym: $i > $i > $o ).
thf(c_List_Olistrel_decl,type,
c_List_Olistrel: $i > $i > $i ).
thf(class_Rings_Ocomm__ring__1_decl,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(c_List_OtakeWhile_decl,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(class_Groups_Ogroup__add_decl,type,
class_Groups_Ogroup__add: $i > $o ).
thf(c_Lattices_Osemilattice__sup__class_Osup_decl,type,
c_Lattices_Osemilattice__sup__class_Osup: $i > $i ).
thf(c_List_OdropWhile_decl,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(c_Rings_Odvd__class_Odvd_decl,type,
c_Rings_Odvd__class_Odvd: $i > $i ).
thf(c_Relation_Oinv__image_decl,type,
c_Relation_Oinv__image: $i > $i > $i ).
thf(c_List_Olexord_decl,type,
c_List_Olexord: $i > $i > $i ).
thf(c_Wellfounded_Oacyclic_decl,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(c_Predicate_Oconversep_decl,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(c_List_Olist_Olist__case_decl,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i ).
thf(c_fNot_decl,type,
c_fNot: $i ).
thf(class_Rings_Osemiring__0_decl,type,
class_Rings_Osemiring__0: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_decl,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(c_Int_Oint__ge__less__than2_decl,type,
c_Int_Oint__ge__less__than2: $i > $i ).
thf(class_Rings_Oring_decl,type,
class_Rings_Oring: $i > $o ).
thf(c_Relation_Oantisym_decl,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(c_Relation_OId_decl,type,
c_Relation_OId: $i > $i ).
thf(c_Nat__Transfer_Ois__nat_decl,type,
c_Nat__Transfer_Ois__nat: $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Rings_Olinordered__semidom_decl,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(c_List_Oupto_decl,type,
c_List_Oupto: $i > $i > $i ).
thf(c_List_Oupto__rel_decl,type,
c_List_Oupto__rel: $i ).
thf(c_List_Olistsp_decl,type,
c_List_Olistsp: $i > $i > $i ).
thf(class_Rings_Odvd_decl,type,
class_Rings_Odvd: $i > $o ).
thf(class_Nat_Osize_decl,type,
class_Nat_Osize: $i > $o ).
thf(tc_Option_Ooption_decl,type,
tc_Option_Ooption: $i > $i ).
thf(c_Hilbert__Choice_OEps_decl,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_List_Oall__interval__nat_decl,type,
c_List_Oall__interval__nat: $i > $i > $i > $o ).
thf(c_Wellfounded_Opred__nat_decl,type,
c_Wellfounded_Opred__nat: $i ).
thf(c_Wellfounded_Omax__ext_decl,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(c_List_Omeasures_decl,type,
c_List_Omeasures: $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequiv_decl,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_Equiv__Relations_Ocongruent2_decl,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Equiv__Relations_Ocongruent_decl,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(c_List_Oall__interval__int_decl,type,
c_List_Oall__interval__int: $i > $i > $i > $o ).
thf(c_List_Oinsert_decl,type,
c_List_Oinsert: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofun__left__comm_decl,type,
c_Finite__Set_Ofun__left__comm: $i > $i > $i > $o ).
thf(c_Lazy__Sequence_Osmall__lazy_H__rel_decl,type,
c_Lazy__Sequence_Osmall__lazy_H__rel: $i ).
thf(c_Finite__Set_Ofold_decl,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(c_Fun_Ofun__upd_decl,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(class_Groups_Ominus_decl,type,
class_Groups_Ominus: $i > $o ).
thf(class_Groups_Oab__semigroup__mult_decl,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(c_Finite__Set_Ofold__image_decl,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Oanamorph_decl,type,
c_Lazy__Sequence_Oanamorph: $i > $i > $i > $i ).
thf(c_Option_Ooption_Ooption__case_decl,type,
c_Option_Ooption_Ooption__case: $i > $i > $i > $i > $i > $i ).
thf(c_Relation_Oirrefl_decl,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_List_Obutlast_decl,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_fdisj_decl,type,
c_fdisj: $i ).
thf(c_Random_Ominus__shift_decl,type,
c_Random_Ominus__shift: $i > $i > $i > $i ).
thf(class_Orderings_Owellorder_decl,type,
class_Orderings_Owellorder: $i > $o ).
thf(c_Code__Numeral_Oint__of_decl,type,
c_Code__Numeral_Oint__of: $i ).
thf(c_List_Olist_Olist__size_decl,type,
c_List_Olist_Olist__size: $i > $i > $i > $i ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(class_Groups_Oab__group__add_decl,type,
class_Groups_Oab__group__add: $i > $o ).
thf(c_Wellfounded_Oless__than_decl,type,
c_Wellfounded_Oless__than: $i ).
thf(c_Orderings_Oord__class_Omax_decl,type,
c_Orderings_Oord__class_Omax: $i > $i ).
thf(class_Lattices_Oboolean__algebra_decl,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(c_Set_Ovimage_decl,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequivp_decl,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(class_Groups_Olinordered__ab__semigroup__add_decl,type,
class_Groups_Olinordered__ab__semigroup__add: $i > $o ).
thf(c_Finite__Set_Ofold__graph_decl,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(class_Enum_Oenum_decl,type,
class_Enum_Oenum: $i > $o ).
thf(tc_Product__Type_Ounit_decl,type,
tc_Product__Type_Ounit: $i ).
thf(c_FunDef_Opair__leq_decl,type,
c_FunDef_Opair__leq: $i ).
thf(c_FunDef_Opair__less_decl,type,
c_FunDef_Opair__less: $i ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_decl,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_Enum_Osublists_decl,type,
c_Enum_Osublists: $i > $i > $i ).
thf(c_Wellfounded_Omeasure_decl,type,
c_Wellfounded_Omeasure: $i > $i ).
thf(class_Lattices_Oab__semigroup__idem__mult_decl,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(c_Finite__Set_Ofold1_decl,type,
c_Finite__Set_Ofold1: $i > $i > $i ).
thf(c_Int_Oint__ge__less__than_decl,type,
c_Int_Oint__ge__less__than: $i > $i ).
thf(c_fTrue_decl,type,
c_fTrue: $i ).
thf(c_fimplies_decl,type,
c_fimplies: $i ).
thf(c_Nat_Onat_Onat__case_decl,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(c_Relation_OId__on_decl,type,
c_Relation_OId__on: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThanLessThan_decl,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Nat_Onat_Onat__rec_decl,type,
c_Nat_Onat_Onat__rec: $i > $i > $i > $i ).
thf(c_Relation_Otrans_decl,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_List_Olex_decl,type,
c_List_Olex: $i > $i > $i ).
thf(c_List_OremoveAll_decl,type,
c_List_OremoveAll: $i > $i > $i ).
thf(c_Nitpick_Oint__gcd_decl,type,
c_Nitpick_Oint__gcd: $i ).
thf(c_List_Omember_decl,type,
c_List_Omember: $i > $i ).
thf(c_Nitpick_Onumber__of__frac_decl,type,
c_Nitpick_Onumber__of__frac: $i > $i > $i ).
thf(c_Nitpick_OAbs__Frac_decl,type,
c_Nitpick_OAbs__Frac: $i > $i > $i ).
thf(c_List_Olist__ex1_decl,type,
c_List_Olist__ex1: $i > $i > $i > $o ).
thf(c_Fun_Othe__inv__into_decl,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_decl,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i ).
thf(c_Typedef_Otype__definition_decl,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_Orderings_Otop__class_Otop_decl,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_Finite__Set_Ofolding__idem_decl,type,
c_Finite__Set_Ofolding__idem: $i > $i > $i > $i > $o ).
thf(c_Product__Type_Ocurry_decl,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i ).
thf(c_Nat__Transfer_Otsub_decl,type,
c_Nat__Transfer_Otsub: $i > $i > $i ).
thf(c_List_Opartition_decl,type,
c_List_Opartition: $i > $i > $i > $i ).
thf(class_Groups_Oordered__ab__group__add_decl,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(c_Wellfounded_Omlex__prod_decl,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Opart__equivp_decl,type,
c_Equiv__Relations_Opart__equivp: $i > $i > $o ).
thf(c_Nitpick_Onorm__frac_decl,type,
c_Nitpick_Onorm__frac: $i > $i > $i ).
thf(c_Relation_OField_decl,type,
c_Relation_OField: $i > $i ).
thf(c_Nitpick_Onorm__frac__rel_decl,type,
c_Nitpick_Onorm__frac__rel: $i ).
thf(class_Finite__Set_Ofinite_decl,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(c_Product__Type_Oprod_Oprod__size_decl,type,
c_Product__Type_Oprod_Oprod__size: $i > $i > $i > $i > $i > $i ).
thf(c_Nat__Transfer_Onat__set_decl,type,
c_Nat__Transfer_Onat__set: $i > $o ).
thf(c_Finite__Set_Ofun__left__comm__idem_decl,type,
c_Finite__Set_Ofun__left__comm__idem: $i > $i > $i > $o ).
thf(c_Enum_Oproduct_decl,type,
c_Enum_Oproduct: $i > $i > $i > $i > $i ).
thf(c_List_Olistrelp_decl,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_decl,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThanAtMost_decl,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_Fun_Obij__betw_decl,type,
c_Fun_Obij__betw: $i > $i > $i > $i > $i > $o ).
thf(c_Hilbert__Choice_Oinv__into_decl,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_FunDef_Omax__strict_decl,type,
c_FunDef_Omax__strict: $i ).
thf(c_New__DSequence_Opos__not__seq_decl,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(c_Lazy__Sequence_Ohb__not__seq_decl,type,
c_Lazy__Sequence_Ohb__not__seq: $i > $i ).
thf(c_List_Oreturn__list_decl,type,
c_List_Oreturn__list: $i > $i ).
thf(c_Relation_Osingle__valued_decl,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_decl,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i ).
thf(c_Orderings_Oord_Omax_decl,type,
c_Orderings_Oord_Omax: $i > $i > $i ).
thf(c_Nitpick_Osetsum_H_decl,type,
c_Nitpick_Osetsum_H: $i > $i > $i > $i > $i ).
thf(c_FunDef_Omin__strict_decl,type,
c_FunDef_Omin__strict: $i ).
thf(c_Wellfounded_Omin__ext_decl,type,
c_Wellfounded_Omin__ext: $i > $i > $i ).
thf(c_Predicate_ODomainP_decl,type,
c_Predicate_ODomainP: $i > $i > $i > $i ).
thf(c_Wellfounded_OwfP_decl,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_Int_ORep__Integ_decl,type,
c_Int_ORep__Integ: $i ).
thf(c_Random_Olog_decl,type,
c_Random_Olog: $i > $i > $i ).
thf(class_Groups_Osgn__if_decl,type,
class_Groups_Osgn__if: $i > $o ).
thf(c_FunDef_Omax__weak_decl,type,
c_FunDef_Omax__weak: $i ).
thf(c_Random_Oiterate_decl,type,
c_Random_Oiterate: $i > $i > $i > $i > $i ).
thf(c_Nitpick_Oone__frac_decl,type,
c_Nitpick_Oone__frac: $i > $i ).
thf(c_HOL_Obool_Obool__size_decl,type,
c_HOL_Obool_Obool__size: $i > $i ).
thf(c_Power_Opower_Opower_decl,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(c_Orderings_Oord_Omin_decl,type,
c_Orderings_Oord_Omin: $i > $i > $i ).
thf(c_Predicate_Oreflp_decl,type,
c_Predicate_Oreflp: $i > $i > $o ).
thf(c_Lazy__Sequence_Osmall__lazy_H_decl,type,
c_Lazy__Sequence_Osmall__lazy_H: $i > $i > $i ).
thf(c_Lazy__Sequence_Oempty_decl,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(c_Lazy__Sequence_Oappend_decl,type,
c_Lazy__Sequence_Oappend: $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Osingle_decl,type,
c_Lazy__Sequence_Osingle: $i > $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Big__Operators_Olattice__class_OInf__fin_decl,type,
c_Big__Operators_Olattice__class_OInf__fin: $i > $i > $i ).
thf(c_Finite__Set_Ofold1Set_decl,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(class_Lattices_Obounded__lattice__bot_decl,type,
class_Lattices_Obounded__lattice__bot: $i > $o ).
thf(c_Finite__Set_Ofolding__image__simple__idem_decl,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Complete__Lattice_OSup__class_OSup_decl,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(c_Big__Operators_Olattice__class_OSup__fin_decl,type,
c_Big__Operators_Olattice__class_OSup__fin: $i > $i > $i ).
thf(c_Product__Type_OSigma_decl,type,
c_Product__Type_OSigma: $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI_decl,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThan_decl,type,
c_SetInterval_Oord__class_OgreaterThan: $i > $i ).
thf(c_Big__Operators_Olinorder__class_OMax_decl,type,
c_Big__Operators_Olinorder__class_OMax: $i > $i > $i ).
thf(c_Finite__Set_Ofolding_decl,type,
c_Finite__Set_Ofolding: $i > $i > $i > $i > $o ).
thf(c_HOL_OEx_decl,type,
c_HOL_OEx: $i > $i ).
thf(c_Big__Operators_Olattice_OSup__fin_decl,type,
c_Big__Operators_Olattice_OSup__fin: $i > $i > $i > $i ).
thf(c_Complete__Lattice_OInf__class_OInf_decl,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(c_Partial__Function_Ofun__lub_decl,type,
c_Partial__Function_Ofun__lub: $i > $i > $i > $i > $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_decl,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_HOL_OAll_decl,type,
c_HOL_OAll: $i > $i ).
thf(c_Set_OPow_decl,type,
c_Set_OPow: $i > $i ).
thf(c_Big__Operators_Olattice_OInf__fin_decl,type,
c_Big__Operators_Olattice_OInf__fin: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeast_decl,type,
c_SetInterval_Oord__class_OatLeast: $i > $i ).
thf(c_SetInterval_Oord_OatLeastAtMost_decl,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatMost_decl,type,
c_SetInterval_Oord__class_OatMost: $i > $i ).
thf(c_Enum_Oenum__class_Oenum__all_decl,type,
c_Enum_Oenum__class_Oenum__all: $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple_decl,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(tc_sum_decl,type,
tc_sum: $i > $i > $i ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeast_decl,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(class_Groups_Ouminus_decl,type,
class_Groups_Ouminus: $i > $o ).
thf(c_Big__Operators_Olinorder__class_OMin_decl,type,
c_Big__Operators_Olinorder__class_OMin: $i > $i > $i ).
thf(c_Finite__Set_Ofolding__one__idem_decl,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_List_Oset__Cons_decl,type,
c_List_Oset__Cons: $i > $i > $i > $i ).
thf(class_Lattices_Obounded__lattice__top_decl,type,
class_Lattices_Obounded__lattice__top: $i > $o ).
thf(c_Int_OInteg_decl,type,
c_Int_OInteg: $i ).
thf(c_SetInterval_Oord_OlessThan_decl,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__one_decl,type,
c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).
thf(c_Equiv__Relations_Oquotient_decl,type,
c_Equiv__Relations_Oquotient: $i > $i ).
thf(c_Partial__Function_Oflat__lub_decl,type,
c_Partial__Function_Oflat__lub: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastLessThan_decl,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_Predicate_OPowp_decl,type,
c_Predicate_OPowp: $i > $i > $i ).
thf(c_Nitpick_Ozero__frac_decl,type,
c_Nitpick_Ozero__frac: $i > $i ).
thf(class_Lattices_Odistrib__lattice_decl,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(c_SetInterval_Oord_OgreaterThanLessThan_decl,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OPlus_decl,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(c_Recdef_Osame__fst_decl,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_decl,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(c_Nitpick_OFrac_decl,type,
c_Nitpick_OFrac: $i ).
thf(c_FunDef_Omin__weak_decl,type,
c_FunDef_Omin__weak: $i ).
thf(c_Set_Othe__elem_decl,type,
c_Set_Othe__elem: $i > $i > $i ).
thf(class_Orderings_Otop_decl,type,
class_Orderings_Otop: $i > $o ).
thf(c_Wellfounded_Ofinite__psubset_decl,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
thf(c_SetInterval_Oord_OgreaterThanAtMost_decl,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(c_FunDef_Oreduction__pair_decl,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_Finite__Set_Ofolding__image_decl,type,
c_Finite__Set_Ofolding__image: $i > $i > $i > $i > $i > $o ).
thf(c_SMT_Oz3div_decl,type,
c_SMT_Oz3div: $i > $i > $i ).
thf(c_Nitpick_Oprod_decl,type,
c_Nitpick_Oprod: $i > $i > $i > $i > $i ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(c_FunDef_Orp__inv__image_decl,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(class_Lattices_Obounded__lattice_decl,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_FunDef_Oin__rel_decl,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(c_Enum_Oenum__class_Oenum__ex_decl,type,
c_Enum_Oenum__class_Oenum__ex: $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_decl,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_SMT_Oz3mod_decl,type,
c_SMT_Oz3mod: $i > $i > $i ).
thf(c_fFalse_decl,type,
c_fFalse: $i ).
thf(c_Hoare__Mirabelle_Opeek__and_decl,type,
c_Hoare__Mirabelle_Opeek__and: $i > $i > $i > $i ).
thf(tc_Com_Ostate_decl,type,
tc_Com_Ostate: $i ).
thf(c_Quotient_OBabs_decl,type,
c_Quotient_OBabs: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThan_decl,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(c_Big__Operators_Ocomm__monoid__big_decl,type,
c_Big__Operators_Ocomm__monoid__big: $i > $i > $i > $i > $i > $o ).
thf(c_Wellfounded_Omax__extp_decl,type,
c_Wellfounded_Omax__extp: $i > $i > $i > $i > $o ).
thf(c_Big__Operators_Osemilattice__big_decl,type,
c_Big__Operators_Osemilattice__big: $i > $i > $i > $o ).
thf(c_Nitpick_Ocard_H_decl,type,
c_Nitpick_Ocard_H: $i > $i > $i ).
thf(c_List_Onat__list_decl,type,
c_List_Onat__list: $i > $o ).
thf(c_New__Random__Sequence_Opos__empty_decl,type,
c_New__Random__Sequence_Opos__empty: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__empty_decl,type,
c_New__DSequence_Opos__empty: $i > $i ).
thf(c_Nitpick_Orefl_H_decl,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_Nitpick_Opair__box_Opair__box__size_decl,type,
c_Nitpick_Opair__box_Opair__box__size: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olistset_decl,type,
c_List_Olistset: $i > $i > $i ).
thf(c_Nitpick_Ofold__graph_H_decl,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Hoare__Mirabelle_Ohoare__valids_decl,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(c_Nitpick_Opair__box_Opair__box__rec_decl,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Oneg__single_decl,type,
c_New__Random__Sequence_Oneg__single: $i > $i ).
thf(c_New__DSequence_Oneg__single_decl,type,
c_New__DSequence_Oneg__single: $i > $i > $i ).
thf(c_New__DSequence_Opos__map_decl,type,
c_New__DSequence_Opos__map: $i > $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Omap_decl,type,
c_Lazy__Sequence_Omap: $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Ohb__single_decl,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(c_New__DSequence_Opos__single_decl,type,
c_New__DSequence_Opos__single: $i > $i > $i ).
thf(c_Set_OBall_decl,type,
c_Set_OBall: $i > $i ).
thf(c_New__Random__Sequence_Opos__union_decl,type,
c_New__Random__Sequence_Opos__union: $i > $i > $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__union_decl,type,
c_New__DSequence_Opos__union: $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__rec_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__case_decl,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__single_decl,type,
c_New__Random__Sequence_Opos__single: $i > $i ).
thf(c_Set_OBex_decl,type,
c_Set_OBex: $i > $i ).
thf(c_New__Random__Sequence_Opos__not__random__dseq_decl,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(c_Product__Type_Oprod_Oprod__rec_decl,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__size_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple__size: $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__case_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple__case: $i > $i > $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
? [B: $i] : ( B @ ( A @ v_P ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] : ( A @ ( sk1 @ v_P ) ) ) ) ).
thf(3838,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__card__le__card__Diff) ).
thf(19887,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3838]) ).
thf(2235,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Oacyclic ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacyclic ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__subset) ).
thf(13373,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Oacyclic ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacyclic ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2235]) ).
thf(3675,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).
thf(19204,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3675]) ).
thf(1366,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
<=> ? [F: $i,G: $i] :
( ( A
= ( G @ ( D @ ( E @ c_List_Ofilter ) @ hAPP ) ) )
& ( B @ ( D @ hAPP ) @ hBOOL )
& ! [H: $i] :
( ( F @ ( E @ c_List_Oset @ hAPP ) @ ( H @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( H @ ( D @ hAPP ) @ hBOOL ) )
& ( C
= ( G @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__eq__Cons__iff) ).
thf(9929,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i,G: $i] :
( ( A
= ( G @ ( D @ ( E @ c_List_Ofilter ) @ hAPP ) ) )
& ( B @ ( D @ hAPP ) @ hBOOL )
& ! [H: $i] :
( ( F @ ( E @ c_List_Oset @ hAPP ) @ ( H @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( H @ ( D @ hAPP ) @ hBOOL ) )
& ( C
= ( G @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
=> ( ( C @ ( D @ ( E @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ? [F: $i,G: $i] :
( ( A
= ( G @ ( D @ ( E @ c_List_Ofilter ) @ hAPP ) ) )
& ( B @ ( D @ hAPP ) @ hBOOL )
& ! [H: $i] :
( ( F @ ( E @ c_List_Oset @ hAPP ) @ ( H @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( H @ ( D @ hAPP ) @ hBOOL ) )
& ( C
= ( G @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(867,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( B @ c_List_Onth @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__setsum__nth) ).
thf(8062,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( B @ c_List_Onth @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(4280,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN__I) ).
thf(21624,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4280]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ c_Code__Numeral_OSuc__code__numeral )
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I3_J) ).
thf(5509,plain,
! [A: $i] :
( ( A @ c_Code__Numeral_OSuc__code__numeral )
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1384,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) )
<=> ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__not__eq__zero) ).
thf(10007,plain,
! [A: $i] :
( ( ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ) )
& ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) )
=> ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(4311,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Olistrelp ) ) ) )
<=> ( ( A @ ( C @ ( E @ ( F @ c_List_Olistrelp ) ) ) )
& ( B @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
thf(21729,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( A @ ( C @ ( E @ ( F @ c_List_Olistrelp ) ) ) )
& ( B @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Olistrelp ) ) ) ) )
& ( ( A @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Olistrelp ) ) ) )
=> ( ( A @ ( C @ ( E @ ( F @ c_List_Olistrelp ) ) ) )
& ( B @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4311]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( C @ c_List_Olist_ONil ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( D @ ( C @ c_List_Olast ) @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__map) ).
thf(6085,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( C @ c_List_Olist_ONil ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( D @ ( C @ c_List_Olast ) @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(2887,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image ) ) ) ) )
=> ( ( C @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( G @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( G @ ( G @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( G @ ( H @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oreindex) ).
thf(16054,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image ) ) ) ) )
=> ( ( C @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( G @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( G @ ( G @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( G @ ( H @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2887]) ).
thf(2656,axiom,
! [A: $i,B: $i] :
( ( ~ ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ c_Divides_Odivmod__nat ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__nat ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ c_Divides_Odivmod__nat ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__if) ).
thf(15170,plain,
! [A: $i,B: $i] :
( ( ~ ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ c_Divides_Odivmod__nat ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__nat ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ c_Divides_Odivmod__nat ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2656]) ).
thf(4012,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnE) ).
thf(20503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4012]) ).
thf(1734,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
thf(11472,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).
thf(1525,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( E @ c_List_Olist__update ) @ ( E @ tc_List_Olist @ ( E @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ ( tc_Nat_Onat @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update_Osimps_I2_J) ).
thf(10609,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( E @ c_List_Olist__update ) @ ( E @ tc_List_Olist @ ( E @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ ( tc_Nat_Onat @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).
thf(2223,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ ( C @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( G @ ( H @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( C @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__compI) ).
thf(13321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ ( C @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( G @ ( H @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( C @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2223]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__map) ).
thf(6387,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(3786,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil @ ( A @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__Suc) ).
thf(19672,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil @ ( A @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3786]) ).
thf(3332,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
thf(17803,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3332]) ).
thf(3521,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(18575,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3521]) ).
thf(189,axiom,
tc_Int_Oint @ class_Rings_Oring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(5382,plain,
tc_Int_Oint @ class_Rings_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__1) ).
thf(4733,plain,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(4734,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(cnf,[status(esa)],[4733]) ).
thf(4735,plain,
! [A: $i] :
( ~ ( A @ class_Rings_Oring__1 )
| ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(lifteq,[status(thm)],[4734]) ).
thf(1,conjecture,
( ? [A: $i,B: $i] : ( B @ ( A @ v_P ) )
=> ? [A: $i,B: $i] : ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ? [A: $i,B: $i] : ( B @ ( A @ v_P ) )
=> ? [A: $i,B: $i] : ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4726,plain,
~ ( ? [A: $i,B: $i] : ( B @ ( A @ v_P ) )
=> ? [A: $i,B: $i] : ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4727,plain,
! [B: $i,A: $i] :
( ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
& ( sk2 @ ( sk1 @ v_P ) ) ),
inference(cnf,[status(esa)],[4726]) ).
thf(4729,plain,
! [B: $i,A: $i] :
~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(cnfConj,[status(thm)],[4727]) ).
thf(23443,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( C @ ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4735,4729]) ).
thf(23460,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= C )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23443]) ).
thf(23487,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23460]) ).
thf(23522,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,23487]) ).
thf(23523,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[23522]) ).
thf(23524,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[23523:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(23549,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[23524]) ).
thf(23563,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) ) )
| ( ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4735,23549]) ).
thf(23565,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= B )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23563]) ).
thf(23577,plain,
! [A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23565]) ).
thf(24712,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,23577]) ).
thf(24713,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[24712]) ).
thf(24714,plain,
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[24713:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(24770,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4735,24714]) ).
thf(24782,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[24770]) ).
thf(24797,plain,
! [A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[24782]) ).
thf(31127,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,24797]) ).
thf(31128,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[31127]) ).
thf(31129,plain,
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[31128:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(3385,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq2) ).
thf(18008,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3385]) ).
thf(2178,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) )
= ( A @ ( B @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Collect__split) ).
thf(13162,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) )
= ( A @ ( B @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2178]) ).
thf(661,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).
thf(7272,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(3262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) )
= ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ c_Set_OCollect @ hAPP ) @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__split) ).
thf(17537,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) )
= ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ c_Set_OCollect @ hAPP ) @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3262]) ).
thf(3992,axiom,
! [A: $i] :
( ( A @ class_Lattices_Oboolean__algebra )
=> ( ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__top__eq) ).
thf(20432,plain,
! [A: $i] :
( ( A @ class_Lattices_Oboolean__algebra )
=> ( ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3992]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I39_J) ).
thf(4835,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(4140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__conj__eq) ).
thf(21040,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4140]) ).
thf(2353,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_OId @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Int__subset) ).
thf(13859,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_OId @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2353]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olexn ) @ hAPP ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= A )
& ( ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn__length) ).
thf(6669,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olexn ) @ hAPP ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= A )
& ( ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(2040,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
<=> ! [D: $i] :
( ( D @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).
thf(12607,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( D @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= D )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ! [D: $i] :
( ( D @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2040]) ).
thf(1729,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
thf(11445,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729]) ).
thf(3100,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oclosed) ).
thf(16928,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3100]) ).
thf(3213,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
thf(17358,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3213]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ? [D: $i] :
( ( D @ ( C @ hAPP ) @ hBOOL )
& ( D @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div_H) ).
thf(5857,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ? [D: $i] :
( ( D @ ( C @ hAPP ) @ hBOOL )
& ( D @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ( ? [D: $i] :
( ( D @ ( C @ hAPP ) @ hBOOL )
& ( D @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(2761,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Osgn__if )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__if) ).
thf(15564,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Osgn__if )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2761]) ).
thf(3814,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(19772,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3814]) ).
thf(3140,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(17072,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3140]) ).
thf(817,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OnegDivAlg ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OnegDivAlg ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OnegDivAlg ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).
thf(7854,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OnegDivAlg ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OnegDivAlg ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OnegDivAlg ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(53,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
thf(4909,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(3379,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( E @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__inj__on) ).
thf(17986,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( E @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3379]) ).
thf(2724,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__def) ).
thf(15418,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2724]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( G @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( F @ ( E @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__comp) ).
thf(7691,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( G @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( F @ ( E @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(1712,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).
thf(11372,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712]) ).
thf(176,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).
thf(5329,plain,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(3868,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( ( A @ ( B @ c_Relation_Oantisym ) )
=> ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Otrans ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__diff__Id) ).
thf(20014,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( ( A @ ( B @ c_Relation_Oantisym ) )
=> ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Otrans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3868]) ).
thf(3301,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__quotient) ).
thf(17684,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3301]) ).
thf(874,axiom,
c_fTrue @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(8089,plain,
c_fTrue @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(3017,axiom,
~ ( c_fFalse @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(16603,plain,
~ ( c_fFalse @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3017]) ).
thf(16604,plain,
~ ( c_fFalse @ hBOOL ),
inference(polarity_switch,[status(thm)],[16603]) ).
thf(26605,plain,
( ( ( c_fFalse @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8089,16604]) ).
thf(26606,plain,
( ( c_fFalse @ hBOOL )
!= ( c_fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[26605]) ).
thf(26625,plain,
c_fFalse != c_fTrue,
inference(simp,[status(thm)],[26606]) ).
thf(1488,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div__lemma) ).
thf(10452,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488]) ).
thf(1904,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinfinite) ).
thf(12116,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1904]) ).
thf(3739,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oord )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__iff) ).
thf(19481,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oord )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3739]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__number__of__def) ).
thf(4773,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4774,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ),
inference(cnf,[status(esa)],[4773]) ).
thf(4775,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ),
inference(lifteq,[status(thm)],[4774]) ).
thf(33305,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(paramod_ordered,[status(thm)],[4775,23549]) ).
thf(33389,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33305]) ).
thf(33616,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33389]) ).
thf(2021,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I7_J) ).
thf(12526,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2021]) ).
thf(3648,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc__atMost) ).
thf(19101,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3648]) ).
thf(4352,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( B @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__trans) ).
thf(21908,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( B @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4352]) ).
thf(4235,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(21439,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4235]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(6712,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(2989,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
thf(16501,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2989]) ).
thf(3636,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [H: $i] :
( ( H @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
& ( B
= ( H @ ( A @ ( E @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).
thf(19062,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [H: $i] :
( ( H @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
& ( B
= ( H @ ( A @ ( E @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3636]) ).
thf(1740,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
thf(11504,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1740]) ).
thf(4275,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Ocommute) ).
thf(21595,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4275]) ).
thf(1173,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I1_J) ).
thf(9180,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(1505,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A )
<=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__iff) ).
thf(10520,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).
thf(3532,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
thf(18610,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3532]) ).
thf(2330,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(13783,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2330]) ).
thf(883,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ c_List_Olist_ONil @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
<=> ( ( ( A @ ( D @ c_List_Olast ) )
= B )
& ( ( A @ ( D @ c_List_Obutlast ) )
= C )
& ( A
!= ( D @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).
thf(8114,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( A @ ( D @ c_List_Olast ) )
= B )
& ( ( A @ ( D @ c_List_Obutlast ) )
= C )
& ( A
!= ( D @ c_List_Olist_ONil ) ) )
=> ( ( D @ c_List_Olist_ONil @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ) )
& ( ( ( D @ c_List_Olist_ONil @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
=> ( ( ( A @ ( D @ c_List_Olast ) )
= B )
& ( ( A @ ( D @ c_List_Obutlast ) )
= C )
& ( A
!= ( D @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1315,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ ( C @ ( B @ c_Random_Oselect ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select) ).
thf(9754,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ ( C @ ( B @ c_Random_Oselect ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(4345,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D = C )
<=> ( E @ ( A @ ( B @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eq__iff) ).
thf(21871,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( A @ ( B @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D = C ) )
& ( ( D = C )
=> ( E @ ( A @ ( B @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4345]) ).
thf(4717,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(23255,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4717]) ).
thf(3951,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
thf(20300,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3951]) ).
thf(4597,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).
thf(22792,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4597]) ).
thf(1336,axiom,
! [A: $i] :
( ( A @ c_List_Oreturn__list )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_return__list__def) ).
thf(9833,plain,
! [A: $i] :
( ( A @ c_List_Oreturn__list )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(3766,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__fold1__iff) ).
thf(19594,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3766]) ).
thf(2155,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__distrib) ).
thf(13058,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2155]) ).
thf(3773,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__semigroup__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__Un) ).
thf(19623,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__semigroup__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3773]) ).
thf(949,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_Oremove1 ) ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__remove1) ).
thf(8338,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_Oremove1 ) ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(1547,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0__le__iff) ).
thf(10730,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547]) ).
thf(614,axiom,
! [A: $i] :
( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Osucc @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__add__1) ).
thf(7100,plain,
! [A: $i] :
( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Osucc @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(4029,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i,F: $i] :
( ( B
= ( E @ ( F @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( F @ ( E @ ( D @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseE) ).
thf(20559,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i,F: $i] :
( ( B
= ( E @ ( F @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( F @ ( E @ ( D @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4029]) ).
thf(915,axiom,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Pls) ).
thf(8225,plain,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(8226,plain,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= c_Int_OPls ),
inference(lifteq,[status(thm)],[8225]) ).
thf(2690,axiom,
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__0) ).
thf(15291,plain,
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2690]) ).
thf(15292,plain,
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
inference(polarity_switch,[status(thm)],[15291]) ).
thf(26603,plain,
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8089,15292]) ).
thf(26604,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[26603]) ).
thf(26629,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ hAPP ) )
!= c_fTrue ),
inference(simp,[status(thm)],[26604]) ).
thf(761,axiom,
( c_Int_OPls
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
thf(7677,plain,
( c_Int_OPls
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(7678,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= c_Int_OPls ),
inference(lifteq,[status(thm)],[7677]) ).
thf(39012,plain,
( ( c_Int_OPls @ ( c_Nat__Numeral_Oneg @ hAPP ) )
!= c_fTrue ),
inference(rewrite,[status(thm)],[26629,7678]) ).
thf(45145,plain,
( ( ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
!= ( c_Int_OPls @ ( c_Nat__Numeral_Oneg @ hAPP ) ) )
| ( c_fTrue != c_Int_OPls ) ),
inference(paramod_ordered,[status(thm)],[8226,39012]) ).
thf(45468,plain,
( ( c_Int_OPls != c_Int_OPls )
| ( ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus )
!= c_Nat__Numeral_Oneg )
| ( c_fTrue != c_Int_OPls ) ),
inference(simp,[status(thm)],[45145]) ).
thf(45790,plain,
( ( ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus )
!= c_Nat__Numeral_Oneg )
| ( c_fTrue != c_Int_OPls ) ),
inference(simp,[status(thm)],[45468]) ).
thf(800,axiom,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ c_Int_Osucc @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__number__of) ).
thf(7798,plain,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ c_Int_Osucc @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(4122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( C @ c_COMBC ) ) @ hAPP ) @ ( C @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__set__fold) ).
thf(20973,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( C @ c_COMBC ) ) @ hAPP ) @ ( C @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4122]) ).
thf(1418,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( E @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
=> ( ( B @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__take__lemma) ).
thf(10134,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( E @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
=> ( ( B @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(2082,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
thf(12753,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2082]) ).
thf(3559,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD1) ).
thf(18761,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3559]) ).
thf(1306,axiom,
~ ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__number__of__Pls) ).
thf(9731,plain,
~ ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(4025,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(20544,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4025]) ).
thf(2374,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I52_J) ).
thf(13933,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2374]) ).
thf(1292,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__minus) ).
thf(9685,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(2073,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ ( B @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__mapD) ).
thf(12731,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ ( B @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2073]) ).
thf(2762,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(15573,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2762]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield__inverse__zero ) )
=> ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral0) ).
thf(5654,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield__inverse__zero ) )
=> ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(4699,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
thf(23194,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4699]) ).
thf(1551,axiom,
tc_Int_Oint @ class_Groups_Osgn__if,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
thf(10743,plain,
tc_Int_Oint @ class_Groups_Osgn__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551]) ).
thf(4416,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
thf(22133,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4416]) ).
thf(470,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
thf(6512,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(2624,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_Divides_Odivmod__nat ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__zero) ).
thf(15055,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_Divides_Odivmod__nat ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2624]) ).
thf(1605,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__append) ).
thf(10944,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605]) ).
thf(3161,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil @ ( A @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__Suc__append) ).
thf(17175,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil @ ( A @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3161]) ).
thf(3382,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty) ).
thf(17998,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3382]) ).
thf(929,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__idem) ).
thf(8266,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(4603,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ominus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(22820,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ominus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4603]) ).
thf(389,axiom,
! [A: $i] : ( A @ tc_Option_Ooption @ class_Nat_Osize ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Nat_Osize) ).
thf(6171,plain,
! [A: $i] : ( A @ tc_Option_Ooption @ class_Nat_Osize ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(6172,plain,
! [A: $i] : ( A @ tc_Option_Ooption @ class_Nat_Osize ),
inference(cnf,[status(esa)],[6171]) ).
thf(3661,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( A
= ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) )
=> ~ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__cases) ).
thf(19148,plain,
! [A: $i] :
~ ! [B: $i] :
( ( A
= ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) )
=> ~ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3661]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Otl @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__tl) ).
thf(6448,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Otl @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(3652,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int1) ).
thf(19117,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3652]) ).
thf(1871,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( F
= ( H @ ( G @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( F @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI2) ).
thf(11998,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( F
= ( H @ ( G @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( F @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1871]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] : ( A @ ( E @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(5778,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( A @ ( E @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL )
=> ? [E: $i] : ( A @ ( E @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0) ).
thf(4739,plain,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4740,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(cnf,[status(esa)],[4739]) ).
thf(4741,plain,
! [A: $i] :
( ~ ( A @ class_Rings_Oring__1 )
| ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[4740]) ).
thf(23446,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4735,4729]) ).
thf(23470,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= B )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23446]) ).
thf(23492,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23470]) ).
thf(23716,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,23492]) ).
thf(23717,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[23716]) ).
thf(23718,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[23717:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(23748,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[23718]) ).
thf(23834,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4741,23748]) ).
thf(23887,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= B )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23834]) ).
thf(23914,plain,
! [A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23887]) ).
thf(1449,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_Olist__size ) ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__conv__listsum) ).
thf(10319,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_Olist__size ) ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).
thf(1289,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).
thf(9676,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(2996,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
thf(16533,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2996]) ).
thf(1347,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__id) ).
thf(9864,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) )
= C )
=> ( ( B
= ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
thf(7072,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) )
= C )
=> ( ( B
= ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(2244,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__member) ).
thf(13405,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2244]) ).
thf(1043,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( D
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( D @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( D @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult1__lemma) ).
thf(8646,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( D
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( D @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( D @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(1463,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I26_J) ).
thf(10363,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(1229,axiom,
! [A: $i] :
( ~ ( A @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__nat) ).
thf(9411,plain,
! [A: $i] :
( ~ ( A @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(1812,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( A @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
thf(11763,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( A @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1812]) ).
thf(3552,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
thf(18723,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3552]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__take) ).
thf(5733,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1698,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(11318,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698]) ).
thf(418,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).
thf(6263,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(990,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Osym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Int__converse) ).
thf(8475,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Osym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(2722,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin__set__fold) ).
thf(15413,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2722]) ).
thf(3899,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(20124,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3899]) ).
thf(4208,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Relation_OImage ) ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__UN) ).
thf(21326,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Relation_OImage ) ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4208]) ).
thf(1616,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
thf(10987,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616]) ).
thf(1714,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
thf(11385,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714]) ).
thf(4728,plain,
sk2 @ ( sk1 @ v_P ),
inference(cnfConj,[status(thm)],[4727]) ).
thf(3416,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( D @ ( E @ tc_prod ) @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cartesian__product) ).
thf(18154,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( D @ ( E @ tc_prod ) @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3416]) ).
thf(1064,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring__0 )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__left__distrib) ).
thf(8755,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring__0 )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(1599,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A )
<=> ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
thf(10901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A ) )
& ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A )
=> ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599]) ).
thf(1748,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A
!= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( B @ c_List_Obutlast ) @ ( B @ c_List_Olinorder__class_Osorted ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__butlast) ).
thf(11527,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A
!= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( B @ c_List_Obutlast ) @ ( B @ c_List_Olinorder__class_Osorted ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1748]) ).
thf(4389,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( A @ ( D @ hAPP ) @ ( C @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(22047,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( A @ ( D @ hAPP ) @ ( C @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4389]) ).
thf(2013,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( C @ ( A @ ( A @ ( B @ ( D @ ( B @ ( D @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( B @ ( B @ tc_prod ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__map__pair__image) ).
thf(12507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( C @ ( A @ ( A @ ( B @ ( D @ ( B @ ( D @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( B @ ( B @ tc_prod ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2013]) ).
thf(2100,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( B @ ( C @ c_COMBC ) ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Collect__split) ).
thf(12812,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( B @ ( C @ c_COMBC ) ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2100]) ).
thf(2603,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).
thf(14944,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2603]) ).
thf(2326,axiom,
( c_Nitpick_OFrac
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Nitpick_Oint__gcd @ ( c_fequal @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_OFrac__def) ).
thf(13768,plain,
( c_Nitpick_OFrac
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Nitpick_Oint__gcd @ ( c_fequal @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2326]) ).
thf(2893,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(16092,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2893]) ).
thf(2712,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image ) ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oeq__fold) ).
thf(15380,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image ) ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2712]) ).
thf(4453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
( ( C
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( D @ c_Relation_OImage ) ) @ hAPP ) ) )
=> ~ ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientE) ).
thf(22257,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
( ( C
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( D @ c_Relation_OImage ) ) @ hAPP ) ) )
=> ~ ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4453]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__idem) ).
thf(8200,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(4126,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).
thf(20990,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4126]) ).
thf(3326,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Wellfounded_Omax__ext ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).
thf(17774,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ c_Wellfounded_Omax__ext ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_Wellfounded_Omax__ext ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3326]) ).
thf(3107,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_List_Olistrel ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( F @ c_List_Olistrel ) @ ( A @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel_OCons) ).
thf(16950,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_List_Olistrel ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( F @ c_List_Olistrel ) @ ( A @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3107]) ).
thf(2932,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( A @ ( C @ c_Wellfounded_Owf ) )
=> ( ( B @ ( A @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__union__compatible) ).
thf(16248,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( A @ ( C @ c_Wellfounded_Owf ) )
=> ( ( B @ ( A @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2932]) ).
thf(2026,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(12549,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2026]) ).
thf(4517,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Diff) ).
thf(22485,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4517]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Orev @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( ( ( B
!= ( C @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( C @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_List_Ofoldr ) ) ) ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__max__sorted) ).
thf(6868,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Orev @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( ( ( B
!= ( C @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( C @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_List_Ofoldr ) ) ) ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(3292,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oinsert ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oinsert__def) ).
thf(17656,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oinsert ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3292]) ).
thf(2010,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).
thf(12500,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2010]) ).
thf(1661,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_List_Olist_ONil @ ( A @ ( C @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__hd__drop) ).
thf(11175,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_List_Olist_ONil @ ( A @ ( C @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__diff) ).
thf(5444,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(2357,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__commute) ).
thf(13869,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2357]) ).
thf(3206,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__zle__neg) ).
thf(17326,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3206]) ).
thf(3545,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI2) ).
thf(18691,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3545]) ).
thf(33140,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( C @ ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(paramod_ordered,[status(thm)],[4775,4729]) ).
thf(33527,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33140]) ).
thf(33754,plain,
! [B: $i,A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33527]) ).
thf(35133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( C @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4735,33754]) ).
thf(35134,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Int_Oint @ class_Rings_Oring__1 ) ),
inference(pattern_uni,[status(thm)],[35133:[bind(A,$thf( tc_Int_Oint )),bind(B,$thf( B )),bind(C,$thf( tc_Int_Oint @ c_Groups_Oone__class_Oone ))]]) ).
thf(35278,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Int_Oint @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[35134]) ).
thf(35876,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[35278,5382]) ).
thf(35877,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[35876]) ).
thf(1212,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).
thf(9342,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(3655,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__inf) ).
thf(19127,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3655]) ).
thf(4667,axiom,
tc_HOL_Obool @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
thf(23056,plain,
tc_HOL_Obool @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4667]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_List_Oupto__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupto ) )
= ( tc_Int_Oint @ c_List_Olist_ONil ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupto ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupto ) @ ( B @ ( tc_Int_Oint @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto_Opsimps) ).
thf(6057,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_List_Oupto__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupto ) )
= ( tc_Int_Oint @ c_List_Olist_ONil ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupto ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupto ) @ ( B @ ( tc_Int_Oint @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(598,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__return__embed) ).
thf(7040,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(2035,axiom,
! [A: $i] :
( ! [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL )
<=> ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat) ).
thf(12575,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) )
=> ! [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL ) )
& ( ! [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL )
=> ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2035]) ).
thf(1133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( A @ ( B @ ( H @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ ( J @ ( I @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( G @ ( H @ ( I @ ( J @ c_Product__Type_Omap__pair ) ) ) ) ) )
= ( A @ ( D @ ( C @ ( H @ ( F @ ( J @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( B @ ( E @ ( G @ ( C @ ( I @ ( F @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( H @ ( J @ tc_prod ) @ ( G @ ( I @ tc_prod ) @ ( C @ ( F @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__compose) ).
thf(9020,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( A @ ( B @ ( H @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ ( J @ ( I @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( G @ ( H @ ( I @ ( J @ c_Product__Type_Omap__pair ) ) ) ) ) )
= ( A @ ( D @ ( C @ ( H @ ( F @ ( J @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( B @ ( E @ ( G @ ( C @ ( I @ ( F @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( H @ ( J @ tc_prod ) @ ( G @ ( I @ tc_prod ) @ ( C @ ( F @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(826,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i,E: $i] :
( ( ( A
= ( E @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__pos__lemma) ).
thf(7888,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ! [D: $i,E: $i] :
( ( ( A
= ( E @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( A
= ( E @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( B
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).
thf(6063,plain,
! [A: $i,B: $i] :
( B
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(2058,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).
thf(12674,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2058]) ).
thf(4448,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( C @ ( F @ ( A @ ( D @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( B @ ( E @ ( A @ ( D @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( G @ c_Fun_Obij__betw ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__Disj__Un) ).
thf(22242,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( C @ ( F @ ( A @ ( D @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( B @ ( E @ ( A @ ( D @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( G @ c_Fun_Obij__betw ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4448]) ).
thf(2627,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
thf(15066,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2627]) ).
thf(3797,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
thf(19713,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3797]) ).
thf(1881,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(12030,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1881]) ).
thf(2797,axiom,
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
thf(15698,plain,
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2797]) ).
thf(1096,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
thf(8883,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(2590,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__trancl) ).
thf(14895,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2590]) ).
thf(4425,axiom,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__singleton) ).
thf(22158,plain,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4425]) ).
thf(2346,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__le__Sup) ).
thf(13834,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2346]) ).
thf(4287,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__div__geq) ).
thf(21645,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4287]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
thf(8129,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_List_Otl @ hAPP ) @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Suc) ).
thf(7935,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_List_Otl @ hAPP ) @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( E @ ( G @ ( C @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ ( C @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__compose) ).
thf(5141,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( E @ ( G @ ( C @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ ( C @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1433,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).
thf(10198,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).
thf(1962,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Wellfounded_Omeasure @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
thf(12334,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Wellfounded_Omeasure @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_Wellfounded_Omeasure @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1962]) ).
thf(2050,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
thf(12649,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2050]) ).
thf(685,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).
thf(7358,plain,
tc_Code__Numeral_Ocode__numeral @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(560,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I2_J) ).
thf(6918,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(4084,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C != B ) )
| ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclD) ).
thf(20798,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C != B ) )
| ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4084]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
thf(8434,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(631,axiom,
! [A: $i] : ( A @ c_Int_Oint__ge__less__than @ ( tc_Int_Oint @ c_Wellfounded_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__int__ge__less__than) ).
thf(7164,plain,
! [A: $i] : ( A @ c_Int_Oint__ge__less__than @ ( tc_Int_Oint @ c_Wellfounded_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1445,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Opartition ) ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_Osnd ) @ hAPP ) )
= ( A @ ( B @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter2) ).
thf(10234,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Opartition ) ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_Osnd ) @ hAPP ) )
= ( A @ ( B @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ c_Product__Type_Osnd ) @ ( E @ ( F @ c_Product__Type_Ofst ) @ ( A @ ( E @ ( F @ tc_prod ) @ ( C @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ tc_prod ) @ ( D @ ( E @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( E @ ( F @ tc_prod ) @ c_COMBS ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( D @ ( E @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__comp__eq) ).
thf(7409,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ c_Product__Type_Osnd ) @ ( E @ ( F @ c_Product__Type_Ofst ) @ ( A @ ( E @ ( F @ tc_prod ) @ ( C @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ tc_prod ) @ ( D @ ( E @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( E @ ( F @ tc_prod ) @ c_COMBS ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( D @ ( E @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(4019,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I10_J) ).
thf(20520,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4019]) ).
thf(4671,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__insert) ).
thf(23065,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4671]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__right) ).
thf(5820,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(4494,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( F @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( ( A @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Fun_Obij__betw ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__combine) ).
thf(22397,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( F @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( ( A @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Fun_Obij__betw ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4494]) ).
thf(4307,axiom,
! [A: $i,B: $i] : ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(21720,plain,
! [A: $i,B: $i] : ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4307]) ).
thf(2311,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_List_Osublist ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__empty) ).
thf(13712,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_List_Osublist ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2311]) ).
thf(588,axiom,
c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Min) ).
thf(7008,plain,
c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(4107,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).
thf(20922,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4107]) ).
thf(4165,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__eq) ).
thf(21149,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4165]) ).
thf(2586,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnionD) ).
thf(14880,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2586]) ).
thf(4075,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).
thf(20748,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4075]) ).
thf(4656,axiom,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Relation_Ototal__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__empty) ).
thf(23021,plain,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Relation_Ototal__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4656]) ).
thf(3473,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(18388,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3473]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__commute) ).
thf(5696,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(4706,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint2) ).
thf(23219,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4706]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( D @ c_List_Olist_ONil ) )
<=> ( C
= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__nonempty) ).
thf(6695,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C
= ( D @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( D @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( D @ c_List_Olist_ONil ) )
=> ( C
= ( D @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(2682,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I3_J) ).
thf(15267,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2682]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(7641,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( C @ ( F @ ( D @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( E @ ( F @ c_Product__Type_Ofst ) @ ( C @ ( D @ tc_prod ) @ ( F @ ( E @ ( F @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( C @ ( D @ c_Product__Type_Ofst ) @ ( B @ ( C @ ( D @ tc_prod ) @ ( F @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__comp__map__pair) ).
thf(6744,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( C @ ( F @ ( D @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( E @ ( F @ c_Product__Type_Ofst ) @ ( C @ ( D @ tc_prod ) @ ( F @ ( E @ ( F @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( C @ ( D @ c_Product__Type_Ofst ) @ ( B @ ( C @ ( D @ tc_prod ) @ ( F @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(166,axiom,
! [A: $i] :
( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OnegDivAlg ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__minus1) ).
thf(5292,plain,
! [A: $i] :
( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OnegDivAlg ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1509,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__power__less__zero) ).
thf(10542,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).
thf(3059,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__induct) ).
thf(16765,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3059]) ).
thf(3424,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__ex1 ) ) )
<=> ( ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_List_Olist__ex1 ) ) ) )
& ( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_fequal @ hAPP ) @ ( C @ ( c_fNot @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fdisj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__all ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex1__simps_I2_J) ).
thf(18193,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_List_Olist__ex1 ) ) ) )
& ( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_fequal @ hAPP ) @ ( C @ ( c_fNot @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fdisj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__all ) ) ) ) )
=> ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__ex1 ) ) ) )
& ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__ex1 ) ) )
=> ( ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_List_Olist__ex1 ) ) ) )
& ( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_fequal @ hAPP ) @ ( C @ ( c_fNot @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fdisj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__all ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3424]) ).
thf(3023,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(16619,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3023]) ).
thf(1532,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( C
= ( D @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mod__eq__lemma) ).
thf(10673,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( C
= ( D @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532]) ).
thf(3077,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(16830,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3077]) ).
thf(2699,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oremove) ).
thf(15314,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2699]) ).
thf(2206,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( C @ ( A @ c_Set_OCollect @ hAPP ) @ ( B @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectI) ).
thf(13255,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( C @ ( A @ c_Set_OCollect @ hAPP ) @ ( B @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2206]) ).
thf(1223,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Oremdups ) )
= A )
<=> ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__id__iff__distinct) ).
thf(9383,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oremdups ) )
= A ) )
& ( ( ( A @ ( B @ c_List_Oremdups ) )
= A )
=> ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(2817,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(15770,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2817]) ).
thf(4572,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Osingleton) ).
thf(22698,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4572]) ).
thf(1238,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
!= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__not__Nil) ).
thf(9456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
!= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(3431,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(18233,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3431]) ).
thf(2947,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Orderings_Olinorder )
& ( C @ class_Complete__Lattice_Ocomplete__lattice ) )
=> ( ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i] :
( ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Sup__iff) ).
thf(16308,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Orderings_Olinorder )
& ( C @ class_Complete__Lattice_Ocomplete__lattice ) )
=> ( ( ? [D: $i] :
( ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2947]) ).
thf(2819,axiom,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) )
= ( B @ c_Orderings_Oord__class_Oless__eq @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OAll @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__Sup) ).
thf(15795,plain,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) )
= ( B @ c_Orderings_Oord__class_Oless__eq @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OAll @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2819]) ).
thf(3490,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__int__atLeastLessThan) ).
thf(18459,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3490]) ).
thf(1721,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Predicate_Oreflp ) )
=> ( A @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflpE) ).
thf(11409,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Predicate_Oreflp ) )
=> ( A @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721]) ).
thf(1516,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Otrans ) )
=> ( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( C @ ( B @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( D @ tc_prod ) @ c_Relation_Otrans ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__lex__prod) ).
thf(10567,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Otrans ) )
=> ( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( C @ ( B @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( D @ tc_prod ) @ c_Relation_Otrans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Osemilattice__sup ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
thf(6813,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Osemilattice__sup ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(3980,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oset @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Set_OCollect @ hAPP ) @ ( C @ tc_List_Olist @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lists__length__le) ).
thf(20400,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oset @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Set_OCollect @ hAPP ) @ ( C @ tc_List_Olist @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3980]) ).
thf(1206,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oidem) ).
thf(9324,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(4055,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(20658,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4055]) ).
thf(3513,axiom,
tc_Int_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
thf(18549,plain,
tc_Int_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3513]) ).
thf(4337,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastAtMost) ).
thf(21849,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4337]) ).
thf(3467,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_Osym ) )
=> ( ( A @ ( C @ c_Relation_Osym ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Osym ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Un) ).
thf(18365,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_Osym ) )
=> ( ( A @ ( C @ c_Relation_Osym ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Osym ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3467]) ).
thf(1080,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__abs) ).
thf(8811,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(1296,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(9704,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(4116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__size ) ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osize_I1_J) ).
thf(20954,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__size ) ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4116]) ).
thf(3956,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ ( F @ c_If @ ( E @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Set_OCollect @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cases) ).
thf(20320,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ ( F @ c_If @ ( E @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Set_OCollect @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3956]) ).
thf(4459,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I11_J) ).
thf(22279,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4459]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( D @ c_List_Orev @ hAPP ) @ ( B @ ( E @ c_List_Orev @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
<=> ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__rev) ).
thf(5297,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
=> ( A @ ( D @ c_List_Orev @ hAPP ) @ ( B @ ( E @ c_List_Orev @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) ) )
& ( ( A @ ( D @ c_List_Orev @ hAPP ) @ ( B @ ( E @ c_List_Orev @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(2823,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(15816,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2823]) ).
thf(2177,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OField @ hAPP ) )
= ( A @ ( B @ ( B @ c_Relation_ORange ) @ hAPP ) @ ( A @ ( B @ ( B @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__def) ).
thf(13159,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OField @ hAPP ) )
= ( A @ ( B @ ( B @ c_Relation_ORange ) @ hAPP ) @ ( A @ ( B @ ( B @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2177]) ).
thf(985,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__upt) ).
thf(8463,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(3730,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(19438,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3730]) ).
thf(2602,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(14937,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2602]) ).
thf(3641,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Times__UNIV) ).
thf(19081,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3641]) ).
thf(2277,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( E
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient) ).
thf(13548,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( E
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2277]) ).
thf(2271,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I6_J) ).
thf(13525,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2271]) ).
thf(2531,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( F @ c_List_Olex ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( F @ c_List_Olex ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( ( D @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__in__lex) ).
thf(14662,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( F @ c_List_Olex ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( ( D @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( F @ c_List_Olex ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( F @ c_List_Olex ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( F @ c_List_Olex ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( ( D @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2531]) ).
thf(2691,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Obot )
=> ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
thf(15293,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Obot )
=> ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2691]) ).
thf(1987,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ocard @ hAPP ) ) )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
thf(12415,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ocard @ hAPP ) ) )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1987]) ).
thf(3367,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).
thf(17929,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3367]) ).
thf(1381,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__diff__distrib__left) ).
thf(9998,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Osort__key ) ) ) )
= ( A @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Osort__key ) ) ) @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sort__key__simps_I2_J) ).
thf(5625,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Osort__key ) ) ) )
= ( A @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Osort__key ) ) ) @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(3720,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ? [D: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter__neutral) ).
thf(19391,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ? [D: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3720]) ).
thf(1301,axiom,
c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of2) ).
thf(9717,plain,
c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(4007,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( E @ ( B @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__surj) ).
thf(20484,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( E @ ( B @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4007]) ).
thf(2088,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(12774,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2088]) ).
thf(689,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 )
= ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
thf(7368,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 )
= ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(3982,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( A @ ( B @ ( C @ ( G @ ( H @ tc_prod ) @ ( D @ ( E @ ( I @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ ( H @ ( I @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( G @ ( H @ ( D @ c_Product__Type_Oscomp ) ) ) @ ( E @ ( F @ ( D @ tc_fun ) @ ( F @ ( G @ tc_fun ) @ ( H @ tc_fun ) @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ tc_fun ) @ ( F @ ( G @ tc_fun ) @ ( H @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( D @ ( E @ ( I @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__scomp) ).
thf(20405,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( A @ ( B @ ( C @ ( G @ ( H @ tc_prod ) @ ( D @ ( E @ ( I @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ ( H @ ( I @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( G @ ( H @ ( D @ c_Product__Type_Oscomp ) ) ) @ ( E @ ( F @ ( D @ tc_fun ) @ ( F @ ( G @ tc_fun ) @ ( H @ tc_fun ) @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ tc_fun ) @ ( F @ ( G @ tc_fun ) @ ( H @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( D @ ( E @ ( I @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3982]) ).
thf(2249,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
thf(13424,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2249]) ).
thf(982,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onorm__frac__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ c_Nitpick_Onorm__frac ) )
= ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( c_Nitpick_Oint__gcd @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ c_Nitpick_Onorm__frac ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Nitpick_Onorm__frac ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Nitpick_Onorm__frac ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Opsimps) ).
thf(8447,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onorm__frac__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ c_Nitpick_Onorm__frac ) )
= ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( c_Nitpick_Oint__gcd @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ c_Nitpick_Onorm__frac ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Nitpick_Onorm__frac ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Nitpick_Onorm__frac ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__nth) ).
thf(8271,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(542,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__div__distrib) ).
thf(6830,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(1243,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( ? [F: $i] :
( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= A )
& ( B
= ( E @ c_List_Olist_ONil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).
thf(9469,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ? [F: $i] :
( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= A )
& ( B
= ( E @ c_List_Olist_ONil ) ) ) )
=> ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ? [F: $i] :
( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= A )
& ( B
= ( E @ c_List_Olist_ONil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(3049,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__converse) ).
thf(16730,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3049]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__setsum) ).
thf(5224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(675,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__mult) ).
thf(7332,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1177,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oremdups ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remdups) ).
thf(9191,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oremdups ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(2462,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
thf(14377,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2462]) ).
thf(4039,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oeq__fold) ).
thf(20601,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4039]) ).
thf(4629,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__mult )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__empty) ).
thf(22910,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__mult )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4629]) ).
thf(3538,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__subset__iff) ).
thf(18635,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oorder )
=> ( ( ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3538]) ).
thf(3133,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat) ).
thf(17046,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3133]) ).
thf(2121,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Partial__Function_Oflat__lub ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OThe ) ) ) )
& ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Partial__Function_Oflat__lub ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_flat__lub__def) ).
thf(12896,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Partial__Function_Oflat__lub ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OThe ) ) ) )
& ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Partial__Function_Oflat__lub ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2121]) ).
thf(2196,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__addf) ).
thf(13227,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2196]) ).
thf(3335,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( D @ ( F @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI2) ).
thf(17815,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( D @ ( F @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3335]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__insert__key) ).
thf(7781,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(1269,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accI) ).
thf(9572,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(3310,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI) ).
thf(17715,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3310]) ).
thf(1015,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).
thf(8563,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(4568,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oempty) ).
thf(22681,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4568]) ).
thf(1415,axiom,
! [A: $i] :
( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).
thf(10125,plain,
! [A: $i] :
( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(1567,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__case__beta) ).
thf(10805,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq) ).
thf(5529,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(4268,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__greatest) ).
thf(21570,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4268]) ).
thf(2338,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__subset) ).
thf(13811,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2338]) ).
thf(3448,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).
thf(18284,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3448]) ).
thf(1801,axiom,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(11724,plain,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1801]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Orev @ hAPP ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I2_J) ).
thf(5383,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Orev @ hAPP ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(4325,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__upper) ).
thf(21812,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4325]) ).
thf(2453,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I4_J) ).
thf(14324,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2453]) ).
thf(1125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Omonoid__add )
=> ( ! [F: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( F @ ( B @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) ) )
=> ( ( C @ ( B @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__map__filter) ).
thf(8988,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Omonoid__add )
=> ( ! [F: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( F @ ( B @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) ) )
=> ( ( C @ ( B @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_List_Orev @ hAPP ) )
= ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
<=> ( B
= ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__singleton__conv) ).
thf(5348,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B
= ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( C @ c_List_Orev @ hAPP ) )
= ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_List_Orev @ hAPP ) )
= ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( B
= ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1317,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__def) ).
thf(9759,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(4332,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ ( F @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ ( D @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Set_Ovimage ) ) @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( F @ c_Set_Oimage ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__split__eq__Sigma) ).
thf(21834,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ ( F @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ ( D @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Set_Ovimage ) ) @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( F @ c_Set_Oimage ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4332]) ).
thf(2764,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted__list__of__set ) )
= ( B @ ( C @ c_List_Olinorder__class_Osorted__list__of__set ) @ ( A @ ( C @ c_List_Oremove1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__remove) ).
thf(15579,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted__list__of__set ) )
= ( B @ ( C @ c_List_Olinorder__class_Osorted__list__of__set ) @ ( A @ ( C @ c_List_Oremove1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2764]) ).
thf(2149,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
thf(13020,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2149]) ).
thf(4521,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oempty) ).
thf(22508,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4521]) ).
thf(3609,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( I @ ( J @ ( K @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( F @ ( G @ ( H @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( D @ ( F @ ( I @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( H @ ( K @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
=> ( ( I @ ( J @ ( K @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( K @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( G @ ( H @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( H @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [L: $i] :
( ( J @ ( L @ ( K @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [M: $i] :
( ( G @ ( M @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( M @ ( L @ ( D @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( D @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( H @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( K @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( H @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( K @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__type2) ).
thf(18942,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( I @ ( J @ ( K @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( F @ ( G @ ( H @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( D @ ( F @ ( I @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( H @ ( K @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
=> ( ( I @ ( J @ ( K @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( K @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( G @ ( H @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( H @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [L: $i] :
( ( J @ ( L @ ( K @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [M: $i] :
( ( G @ ( M @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( M @ ( L @ ( D @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( D @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( H @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( K @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( H @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( K @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3609]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zpower) ).
thf(6732,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(1195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__mult) ).
thf(9268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(3889,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i] :
( ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__below__iff) ).
thf(20081,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ? [D: $i] :
( ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3889]) ).
thf(2188,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(13202,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2188]) ).
thf(396,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod2__gr__0) ).
thf(6194,plain,
! [A: $i] :
( ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(3227,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
thf(17407,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3227]) ).
thf(4314,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ c_List_Olist_ONil @ ( B @ ( A @ c_Enum_On__lists ) ) )
= ( A @ tc_List_Olist @ c_List_Olist_ONil ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ c_List_Olist_ONil @ ( B @ ( A @ c_Enum_On__lists ) ) )
= ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ ( A @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__lists__Nil) ).
thf(21748,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ c_List_Olist_ONil @ ( B @ ( A @ c_Enum_On__lists ) ) )
= ( A @ tc_List_Olist @ c_List_Olist_ONil ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ c_List_Olist_ONil @ ( B @ ( A @ c_Enum_On__lists ) ) )
= ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ ( A @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4314]) ).
thf(3543,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).
thf(18678,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3543]) ).
thf(3953,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ ( F @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( C
= ( D @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( ( B
= ( E @ ( A @ ( G @ ( H @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ( ( C @ ( A @ ( H @ ( F @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( H @ ( G @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex__cong) ).
thf(20305,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ ( F @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( C
= ( D @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( ( B
= ( E @ ( A @ ( G @ ( H @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ( ( C @ ( A @ ( H @ ( F @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( H @ ( G @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3953]) ).
thf(1369,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).
thf(9950,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__take) ).
thf(5501,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(3576,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Osingle__valued ) ) )
<=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).
thf(18824,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E = F ) ) )
=> ( A @ ( B @ ( C @ c_Relation_Osingle__valued ) ) ) )
& ( ( A @ ( B @ ( C @ c_Relation_Osingle__valued ) ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E = F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3576]) ).
thf(4432,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( E @ ( F @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2CI) ).
thf(22185,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( E @ ( F @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4432]) ).
thf(944,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mod__distrib) ).
thf(8320,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(3228,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__drop__subset) ).
thf(17411,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3228]) ).
thf(4022,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( A @ ( B @ ( E @ c_Relation_Orefl__on ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ c_Relation_Orefl__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Int) ).
thf(20537,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( A @ ( B @ ( E @ c_Relation_Orefl__on ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ c_Relation_Orefl__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4022]) ).
thf(2921,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Oof__nat__inject) ).
thf(16196,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ) )
& ( ( ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2921]) ).
thf(3423,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
thf(18184,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3423]) ).
thf(3421,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Set_OCollect @ hAPP ) )
= ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( A @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).
thf(18178,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Set_OCollect @ hAPP ) )
= ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( A @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3421]) ).
thf(4383,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__empty2) ).
thf(22030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4383]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Equiv__Relations_Oequivp ) )
=> ( ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__transp) ).
thf(6971,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Equiv__Relations_Oequivp ) )
=> ( ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(3466,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( C @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= A ) )
& ( ( D
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( C @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__image__times) ).
thf(18356,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( C @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= A ) )
& ( ( D
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( C @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3466]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zmod) ).
thf(6278,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(4348,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(21889,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4348]) ).
thf(1927,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__eq__Nil__conv) ).
thf(12193,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1927]) ).
thf(2185,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBB ) ) @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib2) ).
thf(13187,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBB ) ) @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2185]) ).
thf(3337,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Onth @ hAPP ) @ ( c_fequal @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( B @ c_COMBB ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( B @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( B @ ( tc_Nat_Onat @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__conv__nth) ).
thf(17820,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Onth @ hAPP ) @ ( c_fequal @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( B @ c_COMBB ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( B @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( B @ ( tc_Nat_Onat @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3337]) ).
thf(2986,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
thf(16481,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2986]) ).
thf(4496,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).
thf(22402,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4496]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
thf(8182,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(3591,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [I: $i,J: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [K: $i,L: $i] :
( ( B @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( L @ ( K @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
thf(18878,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [I: $i,J: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [K: $i,L: $i] :
( ( B @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( L @ ( K @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3591]) ).
thf(3630,axiom,
~ ( c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).
thf(19044,plain,
~ ( c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3630]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(6764,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(4141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff2__less) ).
thf(21047,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4141]) ).
thf(1858,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__0) ).
thf(11945,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1858]) ).
thf(467,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).
thf(6505,plain,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(2515,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( H @ tc_prod ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( F @ ( G @ ( H @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( F @ ( C @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__twice) ).
thf(14602,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( H @ tc_prod ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( F @ ( G @ ( H @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( F @ ( C @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2515]) ).
thf(2464,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( E @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( A @ ( E @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__mono) ).
thf(14382,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( E @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( A @ ( E @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2464]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__numeral__1) ).
thf(5565,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1011,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Opartition ) ) )
= ( A @ ( B @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter__conv) ).
thf(8551,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Opartition ) ) )
= ( A @ ( B @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(4547,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( D @ ( B @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__singleton__eq) ).
thf(22599,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( D @ ( B @ hAPP ) )
= A )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4547]) ).
thf(3571,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__iff) ).
thf(18805,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3571]) ).
thf(4540,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv) ).
thf(22579,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4540]) ).
thf(2972,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__greatest) ).
thf(16413,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2972]) ).
thf(3896,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc1) ).
thf(20117,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3896]) ).
thf(769,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(7697,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(3214,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Opartition ) ) )
= ( A @ ( B @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( E @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( E @ c_List_Oset @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__set) ).
thf(17362,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Opartition ) ) )
= ( A @ ( B @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( E @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( E @ c_List_Oset @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3214]) ).
thf(1628,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Relation_Otrans ) )
<=> ( A @ ( B @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__converse) ).
thf(11029,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Relation_Otrans ) ) )
& ( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( B @ c_Relation_Otrans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( tc_Nat_Onat @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__update__nat) ).
thf(5906,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( tc_Nat_Onat @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(3106,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).
thf(16947,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3106]) ).
thf(2068,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__infI1) ).
thf(12714,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2068]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
thf(6675,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(3800,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_fequal @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__noteq) ).
thf(19722,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B != A )
=> ( A @ ( B @ ( c_fequal @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( c_fequal @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3800]) ).
thf(2033,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [D: $i] :
( ( D @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionE) ).
thf(12568,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [D: $i] :
( ( D @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2033]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).
thf(4839,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(4508,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__if) ).
thf(22448,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4508]) ).
thf(1589,axiom,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistrelp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_ONil) ).
thf(10869,plain,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistrelp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589]) ).
thf(2680,axiom,
~ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__int) ).
thf(15262,plain,
~ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2680]) ).
thf(15263,plain,
~ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(polarity_switch,[status(thm)],[15262]) ).
thf(4505,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Big__Operators_Olattice_OSup__fin ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).
thf(22434,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Big__Operators_Olattice_OSup__fin ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4505]) ).
thf(2321,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I7_J) ).
thf(13747,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2321]) ).
thf(2594,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeastAtMost) ).
thf(14905,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2594]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Int_Onat @ hAPP ) )
= A )
<=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff) ).
thf(7556,plain,
! [A: $i,B: $i] :
( ( ( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) )
=> ( ( B @ ( c_Int_Onat @ hAPP ) )
= A ) )
& ( ( ( B @ ( c_Int_Onat @ hAPP ) )
= A )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(1143,axiom,
! [A: $i,B: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__max__length) ).
thf(9052,plain,
! [A: $i,B: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(1592,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Int_Opred @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Bit1) ).
thf(10881,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Int_Opred @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592]) ).
thf(1724,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E != B )
=> ( ( B @ ( A @ ( E @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( E = B )
=> ( ( B @ ( A @ ( E @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update) ).
thf(11417,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E != B )
=> ( ( B @ ( A @ ( E @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( E = B )
=> ( ( B @ ( A @ ( E @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724]) ).
thf(164,axiom,
tc_Int_Oint @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(5288,plain,
tc_Int_Oint @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( D @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).
thf(8915,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( D @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(3595,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(18897,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3595]) ).
thf(1693,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted__list__of__set ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted__list__of__set ) @ ( A @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__insert) ).
thf(11303,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted__list__of__set ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted__list__of__set ) @ ( A @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693]) ).
thf(1898,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(12097,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1898]) ).
thf(955,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Odivmod__int__rel ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ ( c_fNot @ hAPP ) @ ( c_fimplies @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ ( c_fimplies @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_fequal @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__def) ).
thf(8353,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Odivmod__int__rel ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ ( c_fNot @ hAPP ) @ ( c_fimplies @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ ( c_fimplies @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_fequal @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(1458,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).
thf(10346,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(2667,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).
thf(15217,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2667]) ).
thf(994,axiom,
( c_Wellfounded_Oless__than
= ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Otrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__than__def) ).
thf(8489,plain,
( c_Wellfounded_Oless__than
= ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Otrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(8490,plain,
( ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Otrancl ) )
= c_Wellfounded_Oless__than ),
inference(lifteq,[status(thm)],[8489]) ).
thf(2565,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C != B ) )
| ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
thf(14805,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C != B ) )
| ( C = B ) )
=> ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C != B ) )
| ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2565]) ).
thf(2858,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Relation_OId__on ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
thf(15948,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Relation_OId__on ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2858]) ).
thf(2210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_HOL_Obool @ ( F @ ( F @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( F @ ( F @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__I2) ).
thf(13270,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_HOL_Obool @ ( F @ ( F @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( F @ ( F @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2210]) ).
thf(3372,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(17946,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3372]) ).
thf(1626,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__listrel1__converse) ).
thf(11020,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626]) ).
thf(3485,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( F @ ( G @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( G @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( E @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ ( H @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__I) ).
thf(18438,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( F @ ( G @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( G @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( E @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ ( H @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3485]) ).
thf(4042,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( D @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( D @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oreindex) ).
thf(20611,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( D @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( D @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4042]) ).
thf(1543,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Olinorder__class_Osorted__list__of__set ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ( A @ ( B @ c_List_Olinorder__class_Osorted__list__of__set ) @ ( B @ c_List_Olinorder__class_Osorted ) )
& ( ( A @ ( B @ c_List_Olinorder__class_Osorted__list__of__set ) @ ( B @ c_List_Oset @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set) ).
thf(10715,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Olinorder__class_Osorted__list__of__set ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ( A @ ( B @ c_List_Olinorder__class_Osorted__list__of__set ) @ ( B @ c_List_Olinorder__class_Osorted ) )
& ( ( A @ ( B @ c_List_Olinorder__class_Osorted__list__of__set ) @ ( B @ c_List_Oset @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543]) ).
thf(3383,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( F @ c_List_Oset @ hAPP ) @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ c_List_Oset @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__zipE) ).
thf(18001,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( F @ c_List_Oset @ hAPP ) @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ c_List_Oset @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3383]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc2) ).
thf(5316,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(3090,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__vimage__eq__inv__image) ).
thf(16894,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3090]) ).
thf(2647,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Enum_Oenum )
& ( B @ class_Enum_Oenum ) )
=> ( A @ ( B @ tc_prod ) @ class_Enum_Oenum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Enum_Oenum) ).
thf(15130,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Enum_Oenum )
& ( B @ class_Enum_Oenum ) )
=> ( A @ ( B @ tc_prod ) @ class_Enum_Oenum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2647]) ).
thf(3073,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__infinite) ).
thf(16817,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3073]) ).
thf(939,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__Suc) ).
thf(8298,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(2016,axiom,
~ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).
thf(12513,plain,
~ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2016]) ).
thf(12514,plain,
~ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(polarity_switch,[status(thm)],[12513]) ).
thf(29566,plain,
( ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8089,12514]) ).
thf(29567,plain,
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[29566]) ).
thf(29604,plain,
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) )
!= c_fTrue ),
inference(simp,[status(thm)],[29567]) ).
thf(1502,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ofilter ) @ hAPP ) @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( tc_HOL_Obool @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__map) ).
thf(10511,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ofilter ) @ hAPP ) @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( tc_HOL_Obool @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502]) ).
thf(4444,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( G @ c_Nitpick_Ofold__graph_H ) ) ) ) ) )
=> ( A @ ( F @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( C @ ( D @ ( G @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
thf(22225,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( G @ c_Nitpick_Ofold__graph_H ) ) ) ) ) )
=> ( A @ ( F @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( C @ ( D @ ( G @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4444]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(6515,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(4648,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Big__Operators_Olattice_OInf__fin ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).
thf(22987,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Big__Operators_Olattice_OInf__fin ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4648]) ).
thf(1915,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__ge) ).
thf(12158,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1915]) ).
thf(1437,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(10209,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).
thf(3069,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( B @ c_member @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__eq) ).
thf(16804,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( B @ c_member @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3069]) ).
thf(2299,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__subset__Compl__iff) ).
thf(13655,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2299]) ).
thf(2844,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( A @ ( D @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( C = B )
& ( A @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__same) ).
thf(15885,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C = B )
& ( A @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( A @ ( D @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( D @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C = B )
& ( A @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2844]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Ofst ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_COMBK ) @ ( C @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__def) ).
thf(5713,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Ofst ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_COMBK ) @ ( C @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(2307,axiom,
! [A: $i,B: $i] :
( ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) ) )
<=> ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff2) ).
thf(13692,plain,
! [A: $i,B: $i] :
( ( ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) ) ) )
& ( ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) ) )
=> ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2307]) ).
thf(1553,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( ( ( B @ ( A @ ( C @ ( A @ hAPP ) @ ( c_fequal @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( D @ c_List_Ohd @ hAPP ) )
= C )
=> ( ( B @ ( C @ ( D @ c_List_Oremove1 ) ) @ ( C @ ( A @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key__remove1) ).
thf(10747,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( ( ( B @ ( A @ ( C @ ( A @ hAPP ) @ ( c_fequal @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( D @ c_List_Ohd @ hAPP ) )
= C )
=> ( ( B @ ( C @ ( D @ c_List_Oremove1 ) ) @ ( C @ ( A @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553]) ).
thf(4003,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBI @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__def) ).
thf(20468,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBI @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4003]) ).
thf(1217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_COMBI @ ( D @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_COMBI @ ( D @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_COMBI @ ( D @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_COMBI @ ( D @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__left__comm) ).
thf(9356,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_COMBI @ ( D @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_COMBI @ ( D @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_COMBI @ ( D @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_COMBI @ ( D @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(2909,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( B @ c_FunDef_Oin__rel ) ) @ ( B @ c_Wellfounded_OwfP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__in__rel) ).
thf(16150,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( B @ c_FunDef_Oin__rel ) ) @ ( B @ c_Wellfounded_OwfP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2909]) ).
thf(1744,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power2) ).
thf(11513,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744]) ).
thf(1576,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ tc_List_Olist @ c_List_Oreplicate ) ) @ ( B @ c_List_Oconcat ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__replicate__trivial) ).
thf(10827,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ tc_List_Olist @ c_List_Oreplicate ) ) @ ( B @ c_List_Oconcat ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576]) ).
thf(4541,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).
thf(22582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4541]) ).
thf(2963,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__iff) ).
thf(16376,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2963]) ).
thf(2701,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert) ).
thf(15331,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2701]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__take) ).
thf(8385,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(3441,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(18266,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3441]) ).
thf(18267,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(polarity_switch,[status(thm)],[18266]) ).
thf(18268,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(lifteq,[status(thm)],[18267]) ).
thf(39016,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= c_Int_OPls ),
inference(rewrite,[status(thm)],[18268,7678]) ).
thf(3433,axiom,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(18240,plain,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3433]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Obutlast ) @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__butlast) ).
thf(6996,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Obutlast ) @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(3169,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__sup) ).
thf(17202,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3169]) ).
thf(3553,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bex__set__replicate) ).
thf(18729,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B @ ( A @ hAPP ) @ hBOOL ) )
=> ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3553]) ).
thf(3884,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__commute) ).
thf(20066,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3884]) ).
thf(4524,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert__remove) ).
thf(22517,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4524]) ).
thf(1373,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Relation_Osym ) )
<=> ( A @ ( B @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__converse) ).
thf(9961,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Relation_Osym ) )
=> ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Relation_Osym ) ) )
& ( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Relation_Osym ) )
=> ( A @ ( B @ c_Relation_Osym ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(4198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(21285,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4198]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(5178,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(3218,axiom,
! [A: $i] : ( c_FunDef_Omin__weak @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmin__emptyI) ).
thf(17375,plain,
! [A: $i] : ( c_FunDef_Omin__weak @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3218]) ).
thf(2776,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
thf(15611,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2776]) ).
thf(2279,axiom,
~ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__1) ).
thf(13557,plain,
~ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2279]) ).
thf(3113,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( C @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__eq__Range) ).
thf(16965,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( C @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3113]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Orderings_Olinorder )
=> ( ~ ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ ( F @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( E @ ( C @ c_List_Ofilter ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__insort__triv) ).
thf(6894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Orderings_Olinorder )
=> ( ~ ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ ( F @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( E @ ( C @ c_List_Ofilter ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(3647,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oeq__fold_H) ).
thf(19098,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3647]) ).
thf(3835,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
<=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ! [D: $i] :
( ( A @ ( D @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def_H) ).
thf(19863,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ! [D: $i] :
( ( A @ ( D @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) ) )
& ( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ! [D: $i] :
( ( A @ ( D @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3835]) ).
thf(4213,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Odistrib__inf__le) ).
thf(21343,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4213]) ).
thf(3702,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffE) ).
thf(19323,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3702]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Omap__pair ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ c_Product__Type_OPair ) @ ( F @ ( C @ ( E @ tc_prod ) @ ( C @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( E @ tc_prod ) @ ( C @ c_COMBB ) ) @ ( F @ ( C @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ ( C @ ( E @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ tc_prod ) @ ( D @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__def) ).
thf(7980,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Omap__pair ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ c_Product__Type_OPair ) @ ( F @ ( C @ ( E @ tc_prod ) @ ( C @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( E @ tc_prod ) @ ( C @ c_COMBB ) ) @ ( F @ ( C @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ ( C @ ( E @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ tc_prod ) @ ( D @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(2446,axiom,
( c_Int_OMin
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int_OMin__def) ).
thf(14301,plain,
( c_Int_OMin
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2446]) ).
thf(33141,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( C @ ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(paramod_ordered,[status(thm)],[4775,4729]) ).
thf(33468,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33141]) ).
thf(33695,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33468]) ).
thf(551,axiom,
! [A: $i,B: $i] :
( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( c_Int_Onat @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__nat__number__of) ).
thf(6877,plain,
! [A: $i,B: $i] :
( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( c_Int_Onat @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(3673,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
<=> ( ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
& ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un) ).
thf(19191,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
& ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
& ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3673]) ).
thf(3196,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(17285,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3196]) ).
thf(3188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(17258,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3188]) ).
thf(4484,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__disjoint) ).
thf(22365,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4484]) ).
thf(2747,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I8_J) ).
thf(15514,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2747]) ).
thf(3499,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(18499,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3499]) ).
thf(3002,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb1) ).
thf(16555,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3002]) ).
thf(2260,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Equiv__Relations_Ocongruent ) ) ) )
=> ( ( E @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class) ).
thf(13488,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Equiv__Relations_Ocongruent ) ) ) )
=> ( ( E @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2260]) ).
thf(3025,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( A @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__iff) ).
thf(16630,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( A @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3025]) ).
thf(3378,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( D @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_member__rec_I1_J) ).
thf(17976,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ ( D @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3378]) ).
thf(3867,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).
thf(20011,plain,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3867]) ).
thf(4406,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(22101,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4406]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__self) ).
thf(7400,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(599,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit1) ).
thf(7043,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(2042,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__1__Cons) ).
thf(12617,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2042]) ).
thf(742,axiom,
! [A: $i] : ( A @ c_Relation_OId @ ( A @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Id) ).
thf(7605,plain,
! [A: $i] : ( A @ c_Relation_OId @ ( A @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(1275,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(9625,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(2443,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__f) ).
thf(14292,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2443]) ).
thf(1676,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__code__numeral__code) ).
thf(11228,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676]) ).
thf(33143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( v_c @ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(paramod_ordered,[status(thm)],[4775,4729]) ).
thf(33567,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( v_c @ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33143]) ).
thf(33794,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33567]) ).
thf(36773,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4735,33794]) ).
thf(36774,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Int_Oint @ class_Rings_Oring__1 ) ),
inference(pattern_uni,[status(thm)],[36773:[bind(A,$thf( tc_Int_Oint )),bind(B,$thf( tc_Int_Oint @ c_Groups_Oone__class_Oone )),bind(C,$thf( C ))]]) ).
thf(36919,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Int_Oint @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[36774]) ).
thf(37466,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[36919,5382]) ).
thf(37467,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[37466]) ).
thf(2793,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oassoc) ).
thf(15683,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2793]) ).
thf(3182,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
thf(17243,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3182]) ).
thf(2629,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ c_Fun_Oinj__on ) ) ) )
=> ( ! [I: $i] :
( ( C @ ( I @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( I @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( H @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( H @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ ( H @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( F @ ( G @ ( H @ c_Set_Oimage ) ) @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( H @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__INT) ).
thf(15072,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ c_Fun_Oinj__on ) ) ) )
=> ( ! [I: $i] :
( ( C @ ( I @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( I @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( H @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( H @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ ( H @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( F @ ( G @ ( H @ c_Set_Oimage ) ) @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( H @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2629]) ).
thf(4554,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( D @ c_Com_Ocom_OSemi ) @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Comp) ).
thf(22631,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( D @ c_Com_Ocom_OSemi ) @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4554]) ).
thf(3034,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( B @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Relation_OId__on ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__subset__Times) ).
thf(16668,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( B @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Relation_OId__on ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3034]) ).
thf(3541,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Otranspose ) )
= ( B @ tc_List_Olist @ c_List_Olist_ONil ) )
<=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( B @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__empty) ).
thf(18661,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( B @ c_List_Olist_ONil ) ) )
=> ( ( A @ ( B @ c_List_Otranspose ) )
= ( B @ tc_List_Olist @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ c_List_Otranspose ) )
= ( B @ tc_List_Olist @ c_List_Olist_ONil ) )
=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( B @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3541]) ).
thf(4531,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
thf(22547,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4531]) ).
thf(4583,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__empty) ).
thf(22742,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4583]) ).
thf(4489,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_New__Random__Sequence_Opos__union ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ c_New__DSequence_Opos__union ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__union__def) ).
thf(22379,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_New__Random__Sequence_Opos__union ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ c_New__DSequence_Opos__union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4489]) ).
thf(4240,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__acyclic__wf) ).
thf(21467,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4240]) ).
thf(408,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).
thf(6236,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(2384,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A )
<=> ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
thf(13975,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ) )
& ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A )
=> ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2384]) ).
thf(2255,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__Suc) ).
thf(13469,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2255]) ).
thf(2200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(13238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2200]) ).
thf(1454,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power) ).
thf(10336,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(592,axiom,
! [A: $i] :
( ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
<=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__pred__iff__0) ).
thf(7018,plain,
! [A: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(4306,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(21716,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4306]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Oremdups ) )
= ( B @ c_List_Olist_ONil ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__eq__nil__iff) ).
thf(6570,plain,
! [A: $i,B: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Oremdups ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ c_List_Oremdups ) )
= ( B @ c_List_Olist_ONil ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(2498,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un__distrib) ).
thf(14521,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2498]) ).
thf(3510,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
=> ( ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( D @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != D )
=> ( ( D @ ( B @ c_List_Oset @ hAPP ) @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) )
=> ( A @ ( B @ c_List_Oconcat ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__concat) ).
thf(18531,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
=> ( ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( D @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != D )
=> ( ( D @ ( B @ c_List_Oset @ hAPP ) @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) )
=> ( A @ ( B @ c_List_Oconcat ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3510]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ c_Divides_Odivmod__int ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__int__def) ).
thf(5227,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ c_Divides_Odivmod__int ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(3942,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oidem) ).
thf(20280,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3942]) ).
thf(457,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Divides_OposDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos) ).
thf(6466,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Divides_OposDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(2739,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(15482,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2739]) ).
thf(838,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div2__Suc__Suc) ).
thf(7944,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(3085,axiom,
! [A: $i] :
( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) ).
thf(16868,plain,
! [A: $i] :
( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3085]) ).
thf(1146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__base) ).
thf(9064,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2__right) ).
thf(5252,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(346,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(5977,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(3977,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__greater__0__conv) ).
thf(20386,plain,
! [A: $i,B: $i] :
( ( ( A
!= ( B @ c_List_Olist_ONil ) )
=> ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3977]) ).
thf(2783,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
| ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Int) ).
thf(15637,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
| ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2783]) ).
thf(2837,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Un) ).
thf(15863,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2837]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__drop) ).
thf(8086,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(2107,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Nat__Transfer_Ois__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).
thf(12833,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Nat__Transfer_Ois__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2107]) ).
thf(3516,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OField @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ c_Relation_OField @ hAPP ) @ ( B @ ( B @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Field2) ).
thf(18563,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OField @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ c_Relation_OField @ hAPP ) @ ( B @ ( B @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3516]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__exp) ).
thf(6268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__add) ).
thf(5486,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(4057,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
thf(20662,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4057]) ).
thf(1200,axiom,
! [A: $i] :
( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).
thf(9292,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(3405,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( A @ ( B @ ( B @ c_Relation_OImage ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfI__pf) ).
thf(18090,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( A @ ( B @ ( B @ c_Relation_OImage ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3405]) ).
thf(1311,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__semigroup__mult )
=> ( ( B @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__insert__swap) ).
thf(9746,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__semigroup__mult )
=> ( ( B @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(2768,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( F @ ( G @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( F @ ( G @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__imageI) ).
thf(15590,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( F @ ( G @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( F @ ( G @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2768]) ).
thf(3843,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oremove1 ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__idem) ).
thf(19915,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oremove1 ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3843]) ).
thf(4362,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Compl) ).
thf(21948,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4362]) ).
thf(3081,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Relation_OId__on ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__iff) ).
thf(16849,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C = B ) )
=> ( A @ ( D @ c_Relation_OId__on ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_Relation_OId__on ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3081]) ).
thf(4032,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
thf(20569,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4032]) ).
thf(4390,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__empty) ).
thf(22051,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4390]) ).
thf(1753,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( G @ ( E @ ( F @ tc_fun ) @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( F @ ( G @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( F @ ( G @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__comp) ).
thf(11542,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( G @ ( E @ ( F @ tc_fun ) @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( F @ ( G @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( F @ ( G @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753]) ).
thf(2662,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).
thf(15202,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2662]) ).
thf(3911,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Big__Operators_Ocomm__monoid__big ) ) ) ) )
=> ( ( ~ ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= D ) )
& ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
thf(20168,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Big__Operators_Ocomm__monoid__big ) ) ) ) )
=> ( ( ~ ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= D ) )
& ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3911]) ).
thf(606,axiom,
( c_FunDef_Opair__leq
= ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OId @ ( c_FunDef_Opair__less @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leq__def) ).
thf(7079,plain,
( c_FunDef_Opair__leq
= ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OId @ ( c_FunDef_Opair__less @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(3616,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__0) ).
thf(18977,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3616]) ).
thf(1492,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ c_List_Oremdups ) @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oremdups ) )
= ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oremdups ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__map__remdups) ).
thf(10474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ c_List_Oremdups ) @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oremdups ) )
= ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oremdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492]) ).
thf(3024,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
thf(16623,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( A @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3024]) ).
thf(2805,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__apply) ).
thf(15723,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2805]) ).
thf(4712,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).
thf(23236,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4712]) ).
thf(2527,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( B @ ( A @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ c_FunDef_Oreduction__pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pairI) ).
thf(14645,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( B @ ( A @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ c_FunDef_Oreduction__pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2527]) ).
thf(4690,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2E) ).
thf(23130,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4690]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_List_Osublist ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__sublistI) ).
thf(6381,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_List_Osublist ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(4436,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ouminus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ouminus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
thf(22197,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ouminus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ouminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4436]) ).
thf(1852,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_Nat__Transfer_Onat__set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).
thf(11930,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_Nat__Transfer_Onat__set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1852]) ).
thf(1769,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ c_List_Oset @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_OtakeWhile ) ) )
= ( C @ ( B @ ( E @ c_List_OtakeWhile ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__append1) ).
thf(11613,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ c_List_Oset @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_OtakeWhile ) ) )
= ( C @ ( B @ ( E @ c_List_OtakeWhile ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769]) ).
thf(2388,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(13997,plain,
! [A: $i,B: $i] :
( ( B
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2388]) ).
thf(4574,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
thf(22704,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4574]) ).
thf(2204,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__div__less__self) ).
thf(13251,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2204]) ).
thf(3330,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Relation_OField @ hAPP ) @ ( B @ ( C @ c_Relation_OField @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__Field) ).
thf(17798,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Relation_OField @ hAPP ) @ ( B @ ( C @ c_Relation_OField @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3330]) ).
thf(3623,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( F @ c_Wellfounded_Omax__ext ) @ ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_Wellfounded_Omax__ext ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( F @ c_Wellfounded_Omax__ext ) @ ( A @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__additive) ).
thf(19012,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( F @ c_Wellfounded_Omax__ext ) @ ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_Wellfounded_Omax__ext ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( F @ c_Wellfounded_Omax__ext ) @ ( A @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3623]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nitpick_Onumber__of__frac ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ c_Nitpick_OAbs__Frac ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Onumber__of__frac__def) ).
thf(7734,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nitpick_Onumber__of__frac ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ c_Nitpick_OAbs__Frac ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A
!= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( A @ ( B @ c_List_Otl @ hAPP ) @ ( A @ ( B @ c_List_Ohd @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ ( B @ ( B @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__set) ).
thf(7136,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A
!= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( A @ ( B @ c_List_Otl @ hAPP ) @ ( A @ ( B @ c_List_Ohd @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ ( B @ ( B @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(3454,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowD) ).
thf(18304,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3454]) ).
thf(1136,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).
thf(9027,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(2163,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ hAPP ) )
= ( A @ ( D @ ( C @ tc_fun ) @ c_COMBI @ ( D @ ( C @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_fun ) @ c_HOL_OEx @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Complete__Lattice_OInf__class_OInf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__apply) ).
thf(13083,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ hAPP ) )
= ( A @ ( D @ ( C @ tc_fun ) @ c_COMBI @ ( D @ ( C @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_fun ) @ c_HOL_OEx @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Complete__Lattice_OInf__class_OInf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2163]) ).
thf(3832,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
thf(19839,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3832]) ).
thf(1167,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Ohd @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__upt) ).
thf(9159,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Ohd @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(3621,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__finite) ).
thf(18992,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3621]) ).
thf(1380,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__dvd__iff) ).
thf(9994,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).
thf(1402,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).
thf(10071,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(4188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [F: $i] :
( ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__subset__iff) ).
thf(21253,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4188]) ).
thf(3747,axiom,
( ( tc_HOL_Obool @ ( tc_Product__Type_Ounit @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Product__Type_Ounit @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).
thf(19518,plain,
( ( tc_HOL_Obool @ ( tc_Product__Type_Ounit @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Product__Type_Ounit @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3747]) ).
thf(673,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__replicate__trivial) ).
thf(7326,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_OPair ) @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( A @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( A @ c_Random_Oselect__weight ) )
= ( B @ ( A @ c_Random_Oselect ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weigth__select) ).
thf(5056,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_OPair ) @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( A @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( A @ c_Random_Oselect__weight ) )
= ( B @ ( A @ c_Random_Oselect ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
thf(5770,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(989,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).
thf(8472,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(3482,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( B @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__SigmaI) ).
thf(18420,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( B @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3482]) ).
thf(3344,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i] :
( ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__strict__below__iff) ).
thf(17843,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ? [D: $i] :
( ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3344]) ).
thf(2237,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist__all ) ) )
<=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__iff) ).
thf(13378,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Olist__all ) ) ) )
& ( ( A @ ( B @ ( C @ c_List_Olist__all ) ) )
=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2237]) ).
thf(1945,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__max__eq__min) ).
thf(12257,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1945]) ).
thf(2024,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oring )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1__ring) ).
thf(12543,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oring )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2024]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ ( C @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__inv__image) ).
thf(5903,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ ( C @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(3498,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B != A )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ hAPP ) )
!= ( A @ ( D @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
thf(18496,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B != A )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ hAPP ) )
!= ( A @ ( D @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3498]) ).
thf(2937,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).
thf(16268,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2937]) ).
thf(4112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD) ).
thf(20941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4112]) ).
thf(1297,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(9708,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(4669,axiom,
! [A: $i,B: $i,C: $i] : ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).
thf(23060,plain,
! [A: $i,B: $i,C: $i] : ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4669]) ).
thf(2540,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__upt) ).
thf(14716,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2540]) ).
thf(1979,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( D @ ( C @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
thf(12388,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( D @ ( C @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1979]) ).
thf(2692,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI2) ).
thf(15295,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2692]) ).
thf(2609,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib1) ).
thf(14969,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2609]) ).
thf(896,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OposDivAlg ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OposDivAlg ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OposDivAlg ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn__1__number__of) ).
thf(8165,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OposDivAlg ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OposDivAlg ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OposDivAlg ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(3276,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__absorb) ).
thf(17607,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3276]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring__0 )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( D @ ( E @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__const__mult) ).
thf(7343,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring__0 )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( D @ ( E @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1049,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( c_Int_Onat @ ( B @ ( tc_Int_Oint @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( c_Nat__Numeral_Oneg @ ( D @ c_If @ ( tc_Int_Oint @ ( D @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_fun ) @ ( D @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__number__of) ).
thf(8678,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( c_Int_Onat @ ( B @ ( tc_Int_Oint @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( c_Nat__Numeral_Oneg @ ( D @ c_If @ ( tc_Int_Oint @ ( D @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_fun ) @ ( D @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(23791,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4741,23549]) ).
thf(23889,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= B )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23791]) ).
thf(23915,plain,
! [A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23889]) ).
thf(26740,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,23915]) ).
thf(26741,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[26740]) ).
thf(26742,plain,
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[26741:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(39017,plain,
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( c_Int_OPls @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(rewrite,[status(thm)],[26742,7678]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) )
= ( A @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__take) ).
thf(5874,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) )
= ( A @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(1009,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(8546,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(3400,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty) ).
thf(18072,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3400]) ).
thf(2252,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(13447,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2252]) ).
thf(1848,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) ) )
<=> ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff) ).
thf(11912,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) ) )
=> ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1848]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__eq) ).
thf(4758,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4759,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) )
| ~ ( B @ class_Int_Onumber__ring ) ),
inference(cnf,[status(esa)],[4758]) ).
thf(4760,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Int_Onumber__ring )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4759]) ).
thf(3306,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).
thf(17697,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3306]) ).
thf(3973,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__less @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omin__strict @ ( A @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omin__strict @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__insertI) ).
thf(20376,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__less @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omin__strict @ ( A @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omin__strict @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3973]) ).
thf(3314,axiom,
tc_Int_Oint @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).
thf(17727,plain,
tc_Int_Oint @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3314]) ).
thf(4682,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( tc_HOL_Obool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_fNot @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Loop) ).
thf(23112,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( tc_HOL_Obool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_fNot @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4682]) ).
thf(2092,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oremove) ).
thf(12785,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2092]) ).
thf(2194,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono) ).
thf(13223,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2194]) ).
thf(4358,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__append) ).
thf(21935,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4358]) ).
thf(3419,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ class_Enum_Oenum )
& ( D @ class_Orderings_Oorder ) )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__fun_I1_J) ).
thf(18171,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ class_Enum_Oenum )
& ( D @ class_Orderings_Oorder ) )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3419]) ).
thf(1961,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__def) ).
thf(12324,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ c_Relation_Otrans ) ) )
& ( ( A @ ( B @ c_Relation_Otrans ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1961]) ).
thf(2583,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).
thf(14871,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2583]) ).
thf(1225,axiom,
! [A: $i] :
( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Min) ).
thf(9394,plain,
! [A: $i] :
( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oremove1 ) ) @ ( C @ ( D @ c_List_Oremove1 ) ) )
= ( A @ ( C @ ( D @ c_List_Oremove1 ) ) @ ( B @ ( D @ c_List_Oremove1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__commute) ).
thf(5750,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oremove1 ) ) @ ( C @ ( D @ c_List_Oremove1 ) ) )
= ( A @ ( C @ ( D @ c_List_Oremove1 ) ) @ ( B @ ( D @ c_List_Oremove1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(4035,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__mono) ).
thf(20588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4035]) ).
thf(1654,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__eq) ).
thf(11151,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1654]) ).
thf(4401,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__right) ).
thf(22086,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4401]) ).
thf(1887,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastAtMost) ).
thf(12062,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1887]) ).
thf(2643,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int) ).
thf(15119,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2643]) ).
thf(4194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ ( E @ ( F @ ( F @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( F @ ( C @ ( E @ c_COMBC ) ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ ( C @ ( F @ ( F @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__commute) ).
thf(21274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ ( E @ ( F @ ( F @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( F @ ( C @ ( E @ c_COMBC ) ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ ( C @ ( F @ ( F @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4194]) ).
thf(3831,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib) ).
thf(19836,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3831]) ).
thf(1367,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__idom )
=> ( ( C @ ( D @ ( E @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( D @ ( E @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__less) ).
thf(9946,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__idom )
=> ( ( C @ ( D @ ( E @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( D @ ( E @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(3888,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__range) ).
thf(20078,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3888]) ).
thf(1683,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
thf(11250,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683]) ).
thf(3995,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( C @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ c_Relation_OImage ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).
thf(20441,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( C @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ c_Relation_OImage ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3995]) ).
thf(3167,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD2) ).
thf(17197,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3167]) ).
thf(3233,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( ~ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( c_Nat_OSuc @ hAPP ) @ ( A @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cl__ivl__Suc) ).
thf(17428,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( ~ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( c_Nat_OSuc @ hAPP ) @ ( A @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3233]) ).
thf(3921,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).
thf(20209,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3921]) ).
thf(2638,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).
thf(15104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2638]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 @ hAPP ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct1__rotate) ).
thf(5024,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_List_Orotate1 @ hAPP ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_List_Orotate1 @ hAPP ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(299,axiom,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist__all ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__simps_I2_J) ).
thf(5797,plain,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist__all ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult) ).
thf(5342,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( F
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( F @ ( A @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( F @ ( A @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( G @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd1__lemma) ).
thf(8603,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( F
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( F @ ( A @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( F @ ( A @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( G @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(1022,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).
thf(8583,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(4274,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb2) ).
thf(21592,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4274]) ).
thf(3366,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
thf(17925,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3366]) ).
thf(2118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
thf(12879,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) ) )
& ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2118]) ).
thf(2348,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I10_J) ).
thf(13841,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2348]) ).
thf(1981,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__0__I) ).
thf(12394,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1981]) ).
thf(2111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__inter) ).
thf(12843,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2111]) ).
thf(1944,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__left__idem) ).
thf(12254,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1944]) ).
thf(4243,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( c_fequal @ hAPP ) @ ( c_fconj @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( c_fequal @ hAPP ) @ ( c_fconj @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conv__if2) ).
thf(21479,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( c_fequal @ hAPP ) @ ( c_fconj @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( c_fequal @ hAPP ) @ ( c_fconj @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4243]) ).
thf(1967,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SUPI) ).
thf(12351,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1967]) ).
thf(3362,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ ( C @ ( D @ c_COMBC ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( E @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__def) ).
thf(17911,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ ( C @ ( D @ c_COMBC ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( E @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3362]) ).
thf(4067,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( E @ ( F @ ( F @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( F @ ( C @ ( E @ c_COMBC ) ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( C @ ( F @ ( F @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__commute) ).
thf(20707,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( E @ ( F @ ( F @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( F @ ( C @ ( E @ c_COMBC ) ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( C @ ( F @ ( F @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4067]) ).
thf(3557,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
thf(18754,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3557]) ).
thf(3130,axiom,
! [A: $i] :
( ( c_fequal @ ( A @ ( A @ c_Predicate_Oconversep ) ) )
= c_fequal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__eq) ).
thf(17036,plain,
! [A: $i] :
( ( c_fequal @ ( A @ ( A @ c_Predicate_Oconversep ) ) )
= c_fequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3130]) ).
thf(2649,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(15135,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2649]) ).
thf(650,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Osplice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).
thf(7241,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(797,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
thf(7790,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(1608,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
thf(10955,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( F @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( G @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).
thf(6766,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( F @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( G @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(3230,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
thf(17415,plain,
! [A: $i] :
( ( ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3230]) ).
thf(3442,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__E) ).
thf(18269,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3442]) ).
thf(2547,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__atLeastZeroLessThan__int) ).
thf(14737,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2547]) ).
thf(4354,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(21916,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4354]) ).
thf(4130,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
thf(21017,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4130]) ).
thf(2485,axiom,
tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__int) ).
thf(14474,plain,
tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2485]) ).
thf(1638,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( G @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ ( D @ ( F @ ( F @ tc_fun ) @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( F @ ( D @ c_List_Ofoldr ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__map) ).
thf(11068,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( G @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ ( D @ ( F @ ( F @ tc_fun ) @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( F @ ( D @ c_List_Ofoldr ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638]) ).
thf(2002,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).
thf(12475,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002]) ).
thf(2562,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__subset) ).
thf(14793,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2562]) ).
thf(4002,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__inf__insert) ).
thf(20465,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4002]) ).
thf(2304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ hAPP ) )
= ( A @ ( D @ ( C @ tc_fun ) @ c_COMBI @ ( D @ ( C @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_fun ) @ c_HOL_OEx @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Complete__Lattice_OInf__class_OInf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fun__def) ).
thf(13679,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ hAPP ) )
= ( A @ ( D @ ( C @ tc_fun ) @ c_COMBI @ ( D @ ( C @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_fun ) @ c_HOL_OEx @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Complete__Lattice_OInf__class_OInf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2304]) ).
thf(170,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).
thf(5306,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(4024,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Osplice ) ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).
thf(20541,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Osplice ) ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4024]) ).
thf(3277,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Fun_Oid @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__apply) ).
thf(17610,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Fun_Oid @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3277]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__num__frac) ).
thf(6242,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(2645,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(15125,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2645]) ).
thf(1833,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL )
<=> ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__ex) ).
thf(11844,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1833]) ).
thf(2130,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
thf(12943,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2130]) ).
thf(4173,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan__int) ).
thf(21188,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4173]) ).
thf(996,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__left__minus) ).
thf(8494,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(360,axiom,
! [A: $i] : ( A @ c_Relation_OId @ ( A @ c_Relation_Oantisym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id) ).
thf(6039,plain,
! [A: $i] : ( A @ c_Relation_OId @ ( A @ c_Relation_Oantisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(3774,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).
thf(19626,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3774]) ).
thf(1147,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__add__left) ).
thf(9067,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(1521,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).
thf(10587,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( C @ ( D @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
thf(7825,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( C @ ( D @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(13558,plain,
~ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
inference(polarity_switch,[status(thm)],[13557]) ).
thf(4643,axiom,
tc_HOL_Obool @ class_Lattices_Obounded__lattice__bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
thf(22974,plain,
tc_HOL_Obool @ class_Lattices_Obounded__lattice__bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4643]) ).
thf(1126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__left) ).
thf(8996,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__commute) ).
thf(7418,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(3964,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).
thf(20340,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3964]) ).
thf(2671,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__insert) ).
thf(15229,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2671]) ).
thf(2535,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectD) ).
thf(14690,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2535]) ).
thf(2688,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(15286,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2688]) ).
thf(2438,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Obounded__lattice__bot )
=> ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) )
<=> ( ( A
= ( C @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( C @ c_Orderings_Obot__class_Obot ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__eq__bot__iff) ).
thf(14260,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Obounded__lattice__bot )
=> ( ( ( ( A
= ( C @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( C @ c_Orderings_Obot__class_Obot ) ) )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) )
=> ( ( A
= ( C @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( C @ c_Orderings_Obot__class_Obot ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2438]) ).
thf(2342,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oord )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__iff) ).
thf(13821,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oord )
=> ( ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2342]) ).
thf(1233,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(9432,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(2942,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
<=> ( A @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__comp__self) ).
thf(16287,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) )
& ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2942]) ).
thf(4411,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Int) ).
thf(22121,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4411]) ).
thf(1241,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__insort) ).
thf(9464,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(1397,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
thf(10053,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(1379,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I30_J) ).
thf(9988,plain,
! [A: $i] :
( ( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(1782,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__append) ).
thf(11652,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1782]) ).
thf(2135,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__fin__set__fold) ).
thf(12956,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2135]) ).
thf(2456,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_Osym ) )
=> ( ( A @ ( C @ c_Relation_Osym ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Osym ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Int) ).
thf(14351,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_Osym ) )
=> ( ( A @ ( C @ c_Relation_Osym ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Osym ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2456]) ).
thf(1209,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Otl @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Otl @ hAPP ) @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__append2) ).
thf(9332,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Otl @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Otl @ hAPP ) @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(2070,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
thf(12718,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2070]) ).
thf(4330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Wellfounded_Omax__extp ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Ointros) ).
thf(21825,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Wellfounded_Omax__extp ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4330]) ).
thf(2542,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image ) ) ) ) )
=> ( ( C @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( F @ ( G @ ( H @ ( H @ tc_fun ) @ ( H @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ ( G @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Odistrib) ).
thf(14722,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image ) ) ) ) )
=> ( ( C @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( F @ ( G @ ( H @ ( H @ tc_fun ) @ ( H @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ ( G @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2542]) ).
thf(4576,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil) ).
thf(22710,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4576]) ).
thf(512,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__some) ).
thf(6723,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__less__iff) ).
thf(4761,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(727,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ c_Nat__Transfer_Ois__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).
thf(7528,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ c_Nat__Transfer_Ois__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(1623,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
thf(11010,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623]) ).
thf(2815,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice__top ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).
thf(15759,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice__top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2815]) ).
thf(4687,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osimps_I2_J) ).
thf(23123,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4687]) ).
thf(2424,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__insert) ).
thf(14173,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2424]) ).
thf(1643,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( E @ ( C @ ( D @ c_Random_Oiterate ) ) ) @ hAPP ) )
= ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( E @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Random_Oiterate ) ) ) @ ( A @ ( B @ hAPP ) @ ( C @ ( D @ tc_prod ) @ ( C @ ( D @ ( C @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( E @ ( C @ ( D @ c_Random_Oiterate ) ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iterate_Osimps) ).
thf(11087,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( E @ ( C @ ( D @ c_Random_Oiterate ) ) ) @ hAPP ) )
= ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( E @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Random_Oiterate ) ) ) @ ( A @ ( B @ hAPP ) @ ( C @ ( D @ tc_prod ) @ ( C @ ( D @ ( C @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( E @ ( C @ ( D @ c_Random_Oiterate ) ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643]) ).
thf(681,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zmod__mult__2) ).
thf(7349,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(3123,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(17017,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3123]) ).
thf(1587,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Oremdups ) )
= ( A @ ( C @ c_List_Oremdups ) @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__filter) ).
thf(10863,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Oremdups ) )
= ( A @ ( C @ c_List_Oremdups ) @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587]) ).
thf(4593,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I1_J) ).
thf(22777,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4593]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
thf(5064,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(3840,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__inf) ).
thf(19895,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3840]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ! [F: $i] :
( ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( F @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( F @ ( D @ ( E @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( D @ ( A @ ( C @ ( E @ c_List_Olist__all2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__all__nthI) ).
thf(5274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ! [F: $i] :
( ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( F @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( F @ ( D @ ( E @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( D @ ( A @ ( C @ ( E @ c_List_Olist__all2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(6066,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1864,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__absorb1) ).
thf(11966,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1864]) ).
thf(2950,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__insert) ).
thf(16325,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2950]) ).
thf(4341,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__less) ).
thf(21861,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4341]) ).
thf(1441,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I4_J) ).
thf(10221,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(4373,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff1) ).
thf(21985,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4373]) ).
thf(791,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) )
<=> ( A @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort) ).
thf(7771,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) )
& ( ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(4527,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__insert) ).
thf(22536,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4527]) ).
thf(2727,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( E @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( D @ ( B @ hAPP ) )
= ( C @ ( B @ hAPP ) ) ) )
| ( C @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).
thf(15426,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( A @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( D @ ( B @ hAPP ) )
= ( C @ ( B @ hAPP ) ) ) )
| ( C @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ ( E @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ ( E @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( D @ ( B @ hAPP ) )
= ( C @ ( B @ hAPP ) ) ) )
| ( C @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2727]) ).
thf(4218,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).
thf(21354,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) ) )
& ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4218]) ).
thf(4431,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Oneg__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Ohb__single ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
thf(22182,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Oneg__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Ohb__single ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4431]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
thf(7541,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).
thf(6506,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(2417,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oset__Cons ) ) )
= ( A @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olist_OCons @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBB ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ c_COMBS ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__Cons__def) ).
thf(14141,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oset__Cons ) ) )
= ( A @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olist_OCons @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBB ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ c_COMBS ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2417]) ).
thf(2295,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Compl) ).
thf(13636,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2295]) ).
thf(1073,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( B @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ ( B @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ ( B @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__same__conv__map) ).
thf(8785,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( B @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ ( B @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ ( B @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1730,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( B @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( F @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( B @ ( C @ ( A @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2I) ).
thf(11448,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( B @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( F @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( B @ ( C @ ( A @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730]) ).
thf(822,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__card) ).
thf(7877,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(3384,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR2) ).
thf(18005,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3384]) ).
thf(4145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ tc_prod ) @ ( D @ c_COMBB ) ) @ ( C @ ( D @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__def) ).
thf(21064,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ tc_prod ) @ ( D @ c_COMBB ) ) @ ( C @ ( D @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4145]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__le__iff) ).
thf(4776,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4777,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ class_Rings_Olinordered__idom ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ class_Rings_Olinordered__idom ) ) ),
inference(cnf,[status(esa)],[4776]) ).
thf(4778,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ class_Rings_Olinordered__idom ) ),
inference(cnfConj,[status(thm)],[4777]) ).
thf(4584,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_Oantisym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__empty) ).
thf(22745,plain,
! [A: $i] : ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_Oantisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4584]) ).
thf(4614,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).
thf(22859,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4614]) ).
thf(1662,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Odvd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Odvd) ).
thf(11178,plain,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662]) ).
thf(1888,axiom,
( ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__greaterThan__UNIV) ).
thf(12065,plain,
( ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1888]) ).
thf(2788,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__compl) ).
thf(15663,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2788]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__number__of__eq) ).
thf(5150,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(3564,axiom,
! [A: $i] :
( ( c_Int_OInteg @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [B: $i] :
( A
!= ( B @ ( c_Int_ORep__Integ @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__cases) ).
thf(18782,plain,
! [A: $i] :
( ( c_Int_OInteg @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [B: $i] :
( A
!= ( B @ ( c_Int_ORep__Integ @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3564]) ).
thf(3278,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).
thf(17613,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3278]) ).
thf(820,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
thf(7867,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(3044,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__E) ).
thf(16712,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3044]) ).
thf(1363,axiom,
( ( c_Int_OMin @ c_Int_Opred )
= ( c_Int_OMin @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Min) ).
thf(9908,plain,
( ( c_Int_OMin @ c_Int_Opred )
= ( c_Int_OMin @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(9909,plain,
( ( c_Int_OMin @ c_Int_Opred )
= ( c_Int_OMin @ c_Int_OBit0 ) ),
inference(lifteq,[status(thm)],[9908]) ).
thf(3064,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__0R) ).
thf(16789,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3064]) ).
thf(1825,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__conv) ).
thf(11812,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1825]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__minus1__right) ).
thf(5182,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(3834,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ! [E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__iff__nth) ).
thf(19851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ! [E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) )
=> ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3834]) ).
thf(889,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OposDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__1__number__of) ).
thf(8146,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OposDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(1426,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_Osingle__valued ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
thf(10174,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_Osingle__valued ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__power) ).
thf(6662,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(473,axiom,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__code__numeral__def) ).
thf(6521,plain,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(6522,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[6521]) ).
thf(4006,axiom,
( ( tc_Nat_Onat @ c_Orderings_Obot__class_Obot )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__nat__def) ).
thf(20482,plain,
( ( tc_Nat_Onat @ c_Orderings_Obot__class_Obot )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4006]) ).
thf(20483,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( tc_Nat_Onat @ c_Orderings_Obot__class_Obot ) ),
inference(lifteq,[status(thm)],[20482]) ).
thf(47783,plain,
( ( tc_Nat_Onat @ c_Orderings_Obot__class_Obot @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) ),
inference(rewrite,[status(thm)],[6522,20483]) ).
thf(4558,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OemptyI) ).
thf(22640,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4558]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I4_J) ).
thf(6434,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(2103,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OlessThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
thf(12819,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OlessThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OlessThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2103]) ).
thf(4452,axiom,
! [A: $i] :
( ( A @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__empty) ).
thf(22254,plain,
! [A: $i] :
( ( A @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4452]) ).
thf(2818,axiom,
! [A: $i,B: $i] :
( ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) ) )
<=> ( c_Int_Ointrel @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__intrel__iff) ).
thf(15787,plain,
! [A: $i,B: $i] :
( ( ( c_Int_Ointrel @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) ) )
=> ( c_Int_Ointrel @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2818]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rotate1) ).
thf(5289,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(4366,axiom,
! [A: $i,B: $i] :
( ( B
!= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ? [C: $i,D: $i] :
( ~ ( D @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonempty__iff) ).
thf(21960,plain,
! [A: $i,B: $i] :
( ( ? [C: $i,D: $i] :
( ~ ( D @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
=> ( B
!= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( B
!= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ? [C: $i,D: $i] :
( ~ ( D @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4366]) ).
thf(2635,axiom,
! [A: $i] :
( ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__iff) ).
thf(15092,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2635]) ).
thf(3750,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__le) ).
thf(19525,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3750]) ).
thf(2730,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I15_J) ).
thf(15441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2730]) ).
thf(1774,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(11628,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774]) ).
thf(3796,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(19710,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3796]) ).
thf(1872,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
=> ( ( G @ ( C @ ( D @ ( J @ ( J @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( J @ ( J @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ ( B @ ( I @ ( I @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( I @ ( I @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2D) ).
thf(12003,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
=> ( ( G @ ( C @ ( D @ ( J @ ( J @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( J @ ( J @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ ( B @ ( I @ ( I @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( I @ ( I @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1872]) ).
thf(782,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div) ).
thf(7743,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(2681,axiom,
! [A: $i,B: $i] :
~ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).
thf(15264,plain,
! [A: $i,B: $i] :
~ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2681]) ).
thf(4693,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
thf(23140,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4693]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( C @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Product__Type_Ofst ) @ ( C @ ( B @ ( C @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map__fst__snd) ).
thf(5836,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( C @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Product__Type_Ofst ) @ ( C @ ( B @ ( C @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(2633,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
thf(15087,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2633]) ).
thf(1095,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_Enum_Oproduct ) ) ) )
= ( B @ ( C @ tc_prod ) @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_product_Osimps_I1_J) ).
thf(8880,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_Enum_Oproduct ) ) ) )
= ( B @ ( C @ tc_prod ) @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(4014,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
thf(20508,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4014]) ).
thf(4639,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( D @ ( A @ ( C @ ( B @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( D
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( D @ ( A @ ( C @ ( B @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant__conv) ).
thf(22955,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( D @ ( A @ ( C @ ( B @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( D
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( D @ ( A @ ( C @ ( B @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4639]) ).
thf(3986,axiom,
! [A: $i] : ( A @ c_Relation_OId @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Relation_Orefl__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__Id) ).
thf(20418,plain,
! [A: $i] : ( A @ c_Relation_OId @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Relation_Orefl__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3986]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
thf(7665,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(4467,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__left) ).
thf(22304,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4467]) ).
thf(3681,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice__bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
thf(19226,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice__bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3681]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Orotate1 @ hAPP ) )
= ( A @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ohd @ hAPP ) @ ( A @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_List_Otl @ hAPP ) @ ( A @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__hd__tl) ).
thf(5461,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Orotate1 @ hAPP ) )
= ( A @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ohd @ hAPP ) @ ( A @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_List_Otl @ hAPP ) @ ( A @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(4211,axiom,
! [A: $i,B: $i] : ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__length) ).
thf(21339,plain,
! [A: $i,B: $i] : ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4211]) ).
thf(3703,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I4_J) ).
thf(19327,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3703]) ).
thf(2568,axiom,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zless) ).
thf(14830,plain,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2568]) ).
thf(3432,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(18236,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3432]) ).
thf(3096,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__le__add__shift) ).
thf(16919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3096]) ).
thf(1631,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
<=> ( ( ( D @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) ) )
& ( ( D @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__fst__snd__eq) ).
thf(11040,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( D @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) ) )
& ( ( D @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) ) ) )
=> ( D = C ) )
& ( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) ) )
& ( ( D @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1631]) ).
thf(1829,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__number__of) ).
thf(11827,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1829]) ).
thf(3878,axiom,
tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Wellfounded_Owf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__less) ).
thf(20049,plain,
tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Wellfounded_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3878]) ).
thf(925,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Divides_Odivmod__nat ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Ofst ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nat__def) ).
thf(8257,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Divides_Odivmod__nat ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Ofst ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1069,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I1_J) ).
thf(8770,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(3261,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).
thf(17530,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3261]) ).
thf(2423,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i] :
( ( ( D @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= B )
& ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__nth) ).
thf(14164,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( ( D @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= B )
& ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( ( D @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= B )
& ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2423]) ).
thf(3928,axiom,
( ( tc_Nat_Onat @ c_List_Olist_ONil )
= ( tc_Int_Oint @ c_List_Olist_ONil @ c_List_Oreturn__list ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__list__functions_I2_J) ).
thf(20231,plain,
( ( tc_Nat_Onat @ c_List_Olist_ONil )
= ( tc_Int_Oint @ c_List_Olist_ONil @ c_List_Oreturn__list ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3928]) ).
thf(20232,plain,
( ( tc_Int_Oint @ c_List_Olist_ONil @ c_List_Oreturn__list )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[20231]) ).
thf(4542,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__empty) ).
thf(22585,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4542]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus1__even) ).
thf(7835,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_Ototal__on ) ) )
<=> ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__converse) ).
thf(5744,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) )
=> ( A @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_Ototal__on ) ) ) )
& ( ( A @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_Ototal__on ) ) )
=> ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(4404,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_Oconversep ) ) )
= ( A @ ( C @ ( D @ c_Predicate_Oconversep ) ) @ ( B @ ( C @ ( D @ c_Predicate_Oconversep ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__join) ).
thf(22095,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_Oconversep ) ) )
= ( A @ ( C @ ( D @ c_Predicate_Oconversep ) ) @ ( B @ ( C @ ( D @ c_Predicate_Oconversep ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4404]) ).
thf(4668,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OId__on ) )
= ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__empty) ).
thf(23057,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OId__on ) )
= ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4668]) ).
thf(3036,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__bot )
=> ( ( B @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__right) ).
thf(16672,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__bot )
=> ( ( B @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3036]) ).
thf(3983,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I2_J) ).
thf(20408,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3983]) ).
thf(2875,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Odistrib__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf1__distrib) ).
thf(16003,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Odistrib__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2875]) ).
thf(1869,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(11986,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1869]) ).
thf(3047,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( A @ ( c_Int_ORep__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__int__def) ).
thf(16721,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( A @ ( c_Int_ORep__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3047]) ).
thf(3052,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__replicate) ).
thf(16740,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( C = A ) )
=> ( A @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3052]) ).
thf(2490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ c_Fun_Oid @ ( D @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__id) ).
thf(14487,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ c_Fun_Oid @ ( D @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2490]) ).
thf(4226,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).
thf(21394,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4226]) ).
thf(4606,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( C
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( D @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__const) ).
thf(22827,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( C
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( D @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4606]) ).
thf(4221,axiom,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(21367,plain,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4221]) ).
thf(3305,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I10_J) ).
thf(17694,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3305]) ).
thf(2824,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Opartition ) ) )
= ( A @ ( B @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( ! [F: $i] :
( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( F @ ( D @ hAPP ) @ hBOOL ) )
& ! [F: $i] :
( ( B @ ( E @ c_List_Oset @ hAPP ) @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( D @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__P) ).
thf(15819,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Opartition ) ) )
= ( A @ ( B @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( ! [F: $i] :
( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( F @ ( D @ hAPP ) @ hBOOL ) )
& ! [F: $i] :
( ( B @ ( E @ c_List_Oset @ hAPP ) @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( D @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2824]) ).
thf(3412,axiom,
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J) ).
thf(18143,plain,
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3412]) ).
thf(865,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( A @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( A @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).
thf(8054,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( A @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( A @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(4634,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ! [H: $i,I: $i] :
( ( I @ ( H @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [J: $i] :
( ! [K: $i] :
( ( I @ ( K @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( J @ ( K @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( J @ ( H @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ ( B @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conseq12) ).
thf(22938,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ! [H: $i,I: $i] :
( ( I @ ( H @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [J: $i] :
( ! [K: $i] :
( ( I @ ( K @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( J @ ( K @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( J @ ( H @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ ( B @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4634]) ).
thf(3045,axiom,
( ( c_Com_Ocom_OSKIP @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I1_J) ).
thf(16716,plain,
( ( c_Com_Ocom_OSKIP @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3045]) ).
thf(934,axiom,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__0__number__of) ).
thf(8278,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(2390,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Relation_OId @ ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).
thf(14002,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( C @ c_Relation_OId @ ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ c_Relation_OId @ ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2390]) ).
thf(4420,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).
thf(22144,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4420]) ).
thf(2782,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
thf(15633,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2782]) ).
thf(3489,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
<=> ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ ( B @ ( B @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ c_Fun_Oid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff) ).
thf(18451,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ ( B @ ( B @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ c_Fun_Oid ) )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ ( B @ ( B @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ c_Fun_Oid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3489]) ).
thf(3517,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryE) ).
thf(18565,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3517]) ).
thf(3031,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(16655,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3031]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__diff) ).
thf(4730,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4731,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_Rings_Oring__1 ) ),
inference(cnf,[status(esa)],[4730]) ).
thf(4732,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ class_Rings_Oring__1 )
| ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4731]) ).
thf(23313,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( E @ ( v_c @ ( D @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4732,4729]) ).
thf(23337,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= E )
| ( ( C @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( D @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23313]) ).
thf(23346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( D @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23337]) ).
thf(23361,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( D @ ( F @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( E @ ( F @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ( ( F @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( G @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( F @ class_Rings_Oring__1 )
| ~ ( C @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4732,23346]) ).
thf(23362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( D @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ class_Rings_Oring__1 )
| ~ ( C @ class_Rings_Oring__1 ) ),
inference(pattern_uni,[status(thm)],[23361:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B )),bind(F,$thf( C ))]]) ).
thf(23383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( D @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23362]) ).
thf(3854,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Hilbert__Choice_OEps ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__def) ).
thf(19959,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Hilbert__Choice_OEps ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3854]) ).
thf(2126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(12920,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2126]) ).
thf(1507,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__less__iff) ).
thf(10534,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507]) ).
thf(3055,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI2) ).
thf(16757,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3055]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ c_Random_Ominus__shift ) ) )
= ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ c_Random_Ominus__shift ) ) )
= ( B @ ( C @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__shift__def) ).
thf(6681,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ c_Random_Ominus__shift ) ) )
= ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ c_Random_Ominus__shift ) ) )
= ( B @ ( C @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(3535,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_Odivmod__nat ) )
= ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__base) ).
thf(18617,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_Odivmod__nat ) )
= ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3535]) ).
thf(4426,axiom,
! [A: $i,B: $i] :
( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ c_List_Oset @ hAPP ) ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty2) ).
thf(22161,plain,
! [A: $i,B: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ c_List_Oset @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ c_List_Oset @ hAPP ) ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4426]) ).
thf(3298,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
thf(17677,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3298]) ).
thf(1537,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__insort__insert) ).
thf(10687,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).
thf(2524,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__iff) ).
thf(14633,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2524]) ).
thf(1953,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__commute) ).
thf(12291,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1953]) ).
thf(4532,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__empty1) ).
thf(22551,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4532]) ).
thf(2616,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(15028,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2616]) ).
thf(3782,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin__set__fold) ).
thf(19658,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3782]) ).
thf(4718,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__singleton) ).
thf(23258,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4718]) ).
thf(2552,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__int) ).
thf(14758,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2552]) ).
thf(3941,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
thf(20276,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3941]) ).
thf(1582,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I3_J) ).
thf(10850,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582]) ).
thf(1814,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) )
= ( B @ ( A @ ( C @ c_List_Oappend @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ c_List_Otl @ hAPP ) @ ( C @ ( C @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__append) ).
thf(11773,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) )
= ( B @ ( A @ ( C @ c_List_Oappend @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ c_List_Otl @ hAPP ) @ ( C @ ( C @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1814]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__take) ).
thf(6905,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ c_List_Olist_ONil @ ( A @ ( C @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) )
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sort__key__simps_I1_J) ).
thf(5199,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ c_List_Olist_ONil @ ( A @ ( C @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) )
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__dropWhile__id) ).
thf(6396,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(3525,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( A @ ( B @ ( D @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ tc_prod ) @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ tc_prod ) @ ( D @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).
thf(18582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( A @ ( B @ ( D @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ tc_prod ) @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ tc_prod ) @ ( D @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3525]) ).
thf(3969,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__conj) ).
thf(20364,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3969]) ).
thf(3061,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(16772,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3061]) ).
thf(1767,axiom,
! [A: $i] : ( c_fequal @ ( A @ c_Equiv__Relations_Oequivp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_identity__equivp) ).
thf(11609,plain,
! [A: $i] : ( c_fequal @ ( A @ c_Equiv__Relations_Oequivp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767]) ).
thf(3451,axiom,
tc_Com_Ostate @ class_Nat_Osize,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com__Ostate__Nat_Osize) ).
thf(18292,plain,
tc_Com_Ostate @ class_Nat_Osize,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3451]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(6502,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(3134,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
thf(17049,plain,
! [A: $i,B: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3134]) ).
thf(3829,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i,G: $i] :
( ( D
= ( G @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( G @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons2) ).
thf(19827,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i,G: $i] :
( ( D
= ( G @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( G @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3829]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I12_J) ).
thf(5802,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(1743,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(11510,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0) ).
thf(5193,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(2407,axiom,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__self) ).
thf(14103,plain,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2407]) ).
thf(3399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ hAPP ) )
= ( A @ ( D @ ( C @ tc_fun ) @ c_COMBI @ ( D @ ( C @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_fun ) @ c_HOL_OEx @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Complete__Lattice_OSup__class_OSup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fun__def) ).
thf(18069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ hAPP ) )
= ( A @ ( D @ ( C @ tc_fun ) @ c_COMBI @ ( D @ ( C @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_fun ) @ c_HOL_OEx @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Complete__Lattice_OSup__class_OSup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3399]) ).
thf(3680,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__top )
=> ( ( B @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__top__right) ).
thf(19223,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__top )
=> ( ( B @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3680]) ).
thf(1340,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oconcat ) @ ( B @ c_List_Oremdups ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ c_List_Oset @ ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remdups__concat) ).
thf(9843,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oconcat ) @ ( B @ c_List_Oremdups ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ c_List_Oset @ ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(1403,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_COMBI @ ( B @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sort__foldl__insort) ).
thf(10074,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_COMBI @ ( B @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(4402,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(22089,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4402]) ).
thf(987,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__uminus) ).
thf(8468,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] : ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( F @ ( D @ hAPP ) @ ( F @ ( c_Nat_OSuc @ hAPP ) @ ( D @ hAPP ) @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( D @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sequence__trans) ).
thf(6599,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] : ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( F @ ( D @ hAPP ) @ ( F @ ( c_Nat_OSuc @ hAPP ) @ ( D @ hAPP ) @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( D @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(3013,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(16584,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3013]) ).
thf(4518,axiom,
! [A: $i,B: $i,C: $i] : ( tc_HOL_Obool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( c_Com_Ocom_OSKIP @ ( A @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OSkip) ).
thf(22488,plain,
! [A: $i,B: $i,C: $i] : ( tc_HOL_Obool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( c_Com_Ocom_OSKIP @ ( A @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4518]) ).
thf(3873,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_List_Oupto ) )
= ( tc_Int_Oint @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto__empty) ).
thf(20027,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_List_Oupto ) )
= ( tc_Int_Oint @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3873]) ).
thf(1028,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Obutlast ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__butlast) ).
thf(8600,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Obutlast ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1948,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( A @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).
thf(12269,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( A @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1948]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(5622,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__rev) ).
thf(5480,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(4553,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( B @ ( C @ c_Finite__Set_Ofold1 ) ) )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton__def) ).
thf(22627,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( B @ ( C @ c_Finite__Set_Ofold1 ) ) )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4553]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Oremdups ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
<=> ( ( A @ ( B @ c_List_Oremdups ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remdups__eq) ).
thf(6365,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ c_List_Oremdups ) )
= A )
=> ( ( A @ ( B @ c_List_Oremdups ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) )
& ( ( ( A @ ( B @ c_List_Oremdups ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( A @ ( B @ c_List_Oremdups ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(1935,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(12229,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1935]) ).
thf(1649,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).
thf(11115,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649]) ).
thf(1763,axiom,
( ( c_Int_OMin @ c_Int_OBit1 )
= c_Int_OMin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__Min) ).
thf(11600,plain,
( ( c_Int_OMin @ c_Int_OBit1 )
= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763]) ).
thf(1611,axiom,
! [A: $i,B: $i,C: $i] :
( C
= ( C @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surjective__pairing) ).
thf(10967,plain,
! [A: $i,B: $i,C: $i] :
( C
= ( C @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611]) ).
thf(3483,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D != B )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I4_J) ).
thf(18424,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D != B )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3483]) ).
thf(1806,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__snoc) ).
thf(11741,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1806]) ).
thf(1180,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( B @ c_Divides_Opdivmod ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBB ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_fequal @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBS ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Divides_Opdivmod ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ ( c_fconj @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ ( c_fconj @ hAPP ) @ hAPP ) @ ( c_fdisj @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__pdivmod) ).
thf(9199,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( B @ c_Divides_Opdivmod ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBB ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_fequal @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBS ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Divides_Opdivmod ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ ( c_fconj @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ ( c_fconj @ hAPP ) @ hAPP ) @ ( c_fdisj @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(3618,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(18982,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3618]) ).
thf(1033,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(8615,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(36767,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4741,33794]) ).
thf(36768,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Int_Oint @ class_Rings_Oring__1 ) ),
inference(pattern_uni,[status(thm)],[36767:[bind(A,$thf( tc_Int_Oint )),bind(B,$thf( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )),bind(C,$thf( C ))]]) ).
thf(36916,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Int_Oint @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[36768]) ).
thf(36948,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[36916,5382]) ).
thf(36949,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[36948]) ).
thf(39006,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( c_Int_OPls @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(rewrite,[status(thm)],[36949,7678]) ).
thf(1219,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__int) ).
thf(9362,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(777,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).
thf(7728,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(1008,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil) ).
thf(8543,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Wellfounded_Oacc ) @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accD) ).
thf(5829,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Wellfounded_Oacc ) @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(2927,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I7_J) ).
thf(16223,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2927]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Predicate_Oconversep ) ) @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ c_Wellfounded_Oacyclic ) )
<=> ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicP__converse) ).
thf(5942,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ ( B @ c_Predicate_Oconversep ) ) @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ c_Wellfounded_Oacyclic ) ) )
& ( ( A @ ( B @ ( B @ c_Predicate_Oconversep ) ) @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ c_Wellfounded_Oacyclic ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(23561,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4735,23549]) ).
thf(23570,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23561]) ).
thf(23580,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23570]) ).
thf(24951,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,23580]) ).
thf(24952,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[24951]) ).
thf(24953,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[24952:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(25000,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[24953]) ).
thf(25017,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4741,25000]) ).
thf(25043,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= B )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[25017]) ).
thf(25051,plain,
! [A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[25043]) ).
thf(31449,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,25051]) ).
thf(31450,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[31449]) ).
thf(31451,plain,
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[31450:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(39023,plain,
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( c_Int_OPls @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(rewrite,[status(thm)],[31451,7678]) ).
thf(4051,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bijI) ).
thf(20647,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4051]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield__inverse__zero ) )
=> ( ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__minus1) ).
thf(4952,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield__inverse__zero ) )
=> ( ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(913,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(8220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(2639,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(15110,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2639]) ).
thf(4520,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_sum ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).
thf(22498,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_sum ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_sum ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4520]) ).
thf(2513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__Compl__subset) ).
thf(14597,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2513]) ).
thf(3583,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ounion__inter) ).
thf(18856,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3583]) ).
thf(2143,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I5_J) ).
thf(12988,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2143]) ).
thf(2967,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ ( G @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ ( G @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib) ).
thf(16394,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ ( G @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ ( G @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2967]) ).
thf(2838,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Diff__distrib1) ).
thf(15866,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2838]) ).
thf(3660,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__0__conv) ).
thf(19140,plain,
! [A: $i,B: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3660]) ).
thf(1304,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__int) ).
thf(9725,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(6828,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(4658,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__empty) ).
thf(23026,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4658]) ).
thf(3656,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(19130,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3656]) ).
thf(1473,axiom,
~ ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I3_J) ).
thf(10403,plain,
~ ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(10404,plain,
~ ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(polarity_switch,[status(thm)],[10403]) ).
thf(26611,plain,
( ( ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8089,10404]) ).
thf(26612,plain,
( ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[26611]) ).
thf(26634,plain,
( ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) )
!= c_fTrue ),
inference(simp,[status(thm)],[26612]) ).
thf(2703,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib1) ).
thf(15338,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2703]) ).
thf(3027,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Odistrib) ).
thf(16640,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3027]) ).
thf(992,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I4_J) ).
thf(8483,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(4538,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I1_J) ).
thf(22568,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4538]) ).
thf(2655,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert__remove) ).
thf(15167,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2655]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( D @ c_Int_Oring__1__class_Oof__int @ ( C @ ( D @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__setsum) ).
thf(4793,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( D @ c_Int_Oring__1__class_Oof__int @ ( C @ ( D @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(2450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI) ).
thf(14316,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2450]) ).
thf(4477,axiom,
! [A: $i,B: $i,C: $i] : ( tc_HOL_Obool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( c_Com_Ocom_OSKIP @ ( A @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I7_J) ).
thf(22338,plain,
! [A: $i,B: $i,C: $i] : ( tc_HOL_Obool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( c_Com_Ocom_OSKIP @ ( A @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4477]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ ( C @ c_List_Olinorder__class_Osort__key ) ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__sort) ).
thf(5020,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( C @ c_List_Olinorder__class_Osort__key ) ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ ( C @ c_List_Olinorder__class_Osort__key ) ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I13_J) ).
thf(7965,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(3242,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negD) ).
thf(17459,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3242]) ).
thf(4422,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
thf(22150,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4422]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__foldl__cons) ).
thf(5077,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(248,axiom,
tc_Int_Oint @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
thf(5617,plain,
tc_Int_Oint @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(4083,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conv__if) ).
thf(20790,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4083]) ).
thf(3550,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I5_J) ).
thf(18713,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3550]) ).
thf(595,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converse) ).
thf(7032,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(719,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( B @ c_List_Olexord ) @ ( B @ tc_List_Olist @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__transI) ).
thf(7509,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( B @ c_List_Olexord ) @ ( B @ tc_List_Olist @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(3347,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__times__insert) ).
thf(17855,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3347]) ).
thf(4160,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( ( A @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ ( A @ c_Orderings_Oord_Omax ) )
= ( A @ c_Orderings_Oord__class_Omin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dual__max) ).
thf(21128,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( ( A @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ ( A @ c_Orderings_Oord_Omax ) )
= ( A @ c_Orderings_Oord__class_Omin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4160]) ).
thf(2581,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
thf(14864,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2581]) ).
thf(3304,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olists ) )
= ( A @ ( B @ c_List_Oset @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__eq__set) ).
thf(17691,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olists ) )
= ( A @ ( B @ c_List_Oset @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3304]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__map) ).
thf(4967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(2312,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Groups_Ocomm__monoid__mult )
& ( C @ class_Groups_Ocomm__monoid__add ) )
=> ( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( A @ ( tc_Nat_Onat @ ( C @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I1_J) ).
thf(13715,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Groups_Ocomm__monoid__mult )
& ( C @ class_Groups_Ocomm__monoid__add ) )
=> ( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( A @ ( tc_Nat_Onat @ ( C @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2312]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(7309,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(2091,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV2) ).
thf(12782,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2091]) ).
thf(1557,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Predicate_Opred__comp ) ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [H: $i] :
( ( A @ ( H @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( H @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
thf(10764,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( A @ ( H @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( H @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Predicate_Opred__comp ) ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Predicate_Opred__comp ) ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [H: $i] :
( ( A @ ( H @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( H @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557]) ).
thf(2117,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Union) ).
thf(12875,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2117]) ).
thf(4338,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).
thf(21852,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4338]) ).
thf(2332,axiom,
! [A: $i] : ( A @ tc_List_Olist @ class_Nat_Osize ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List__Olist__Nat_Osize) ).
thf(13788,plain,
! [A: $i] : ( A @ tc_List_Olist @ class_Nat_Osize ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2332]) ).
thf(3420,axiom,
! [A: $i] :
( ( A
!= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( c_FunDef_Omin__strict @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__emptyI) ).
thf(18175,plain,
! [A: $i] :
( ( A
!= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( c_FunDef_Omin__strict @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3420]) ).
thf(3469,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetD) ).
thf(18370,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3469]) ).
thf(2257,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).
thf(13474,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2257]) ).
thf(2860,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(15954,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2860]) ).
thf(1938,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(12236,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1938]) ).
thf(1924,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olistrel1 ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I2) ).
thf(12185,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olistrel1 ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1924]) ).
thf(3294,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( A @ ( F @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( E @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
thf(17667,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( A @ ( F @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( E @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3294]) ).
thf(3676,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(19206,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3676]) ).
thf(3290,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(17652,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3290]) ).
thf(1279,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__append1) ).
thf(9636,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(4034,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(20579,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4034]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(5787,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(4499,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert) ).
thf(22410,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4499]) ).
thf(1345,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
thf(9854,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A )
=> ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(4516,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
thf(22481,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4516]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Osemiring__1 )
& ( D @ class_Groups_Ocomm__monoid__mult ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__setprod) ).
thf(5264,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Osemiring__1 )
& ( D @ class_Groups_Ocomm__monoid__mult ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1203,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__nat__number__of__number__of) ).
thf(9304,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(1201,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Olist_ONil @ ( B @ ( B @ tc_List_Olist @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( B @ tc_List_Olist @ tc_List_Olist @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Oconcat ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( B @ c_List_Otl @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__filter__tail) ).
thf(9298,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Olist_ONil @ ( B @ ( B @ tc_List_Olist @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( B @ tc_List_Olist @ tc_List_Olist @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Oconcat ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( B @ c_List_Otl @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(3477,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0) ).
thf(18407,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3477]) ).
thf(2885,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Product__Type_OPair ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ c_COMBC ) ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( D @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__product) ).
thf(16050,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Product__Type_OPair ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ c_COMBC ) ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( D @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2885]) ).
thf(2626,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(15060,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2626]) ).
thf(798,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( D @ ( F @ c_List_Oset @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( E @ ( B @ ( C @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( C @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__fun__upd) ).
thf(7792,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( D @ ( F @ c_List_Oset @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( E @ ( B @ ( C @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( C @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(4501,axiom,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
thf(22416,plain,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4501]) ).
thf(1572,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__even__eq) ).
thf(10818,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( E @ hAPP ) )
= C )
=> ( ( C @ ( D @ ( E @ ( A @ ( B @ c_Fun_Ofun__upd ) ) ) ) )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(7786,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( E @ hAPP ) )
= C )
=> ( ( C @ ( D @ ( E @ ( A @ ( B @ c_Fun_Ofun__upd ) ) ) ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(2718,axiom,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__zle__int) ).
thf(15398,plain,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2718]) ).
thf(625,axiom,
~ ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I20_J) ).
thf(7144,plain,
~ ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(4481,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(22357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4481]) ).
thf(964,axiom,
! [A: $i] :
( ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__nat__of) ).
thf(8379,plain,
! [A: $i] :
( ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(1211,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__rotate) ).
thf(9336,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(3972,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
thf(20373,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3972]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( C @ ( F @ ( D @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( E @ ( F @ c_Product__Type_Osnd ) @ ( C @ ( D @ tc_prod ) @ ( E @ ( E @ ( F @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( C @ ( D @ c_Product__Type_Osnd ) @ ( A @ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__comp__map__pair) ).
thf(6227,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( C @ ( F @ ( D @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( E @ ( F @ c_Product__Type_Osnd ) @ ( C @ ( D @ tc_prod ) @ ( E @ ( E @ ( F @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( C @ ( D @ c_Product__Type_Osnd ) @ ( A @ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Orev @ hAPP ) @ ( A @ c_List_Ohd @ hAPP ) )
= ( B @ ( A @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__rev) ).
thf(5526,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Orev @ hAPP ) @ ( A @ c_List_Ohd @ hAPP ) )
= ( B @ ( A @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1972,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( F @ ( E @ c_Relation_Oconverse ) @ hAPP ) @ ( E @ ( F @ c_Relation_Osingle__valued ) ) )
=> ( ( C
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( D @ ( F @ ( E @ c_Relation_OImage ) ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__INT__eq) ).
thf(12362,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( F @ ( E @ c_Relation_Oconverse ) @ hAPP ) @ ( E @ ( F @ c_Relation_Osingle__valued ) ) )
=> ( ( C
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( D @ ( F @ ( E @ c_Relation_OImage ) ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1972]) ).
thf(1353,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Equiv__Relations_Opart__equivp ) )
=> ( ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__transp) ).
thf(9882,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Equiv__Relations_Opart__equivp ) )
=> ( ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(1636,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( E @ c_Relation_Osingle__valued ) ) )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
thf(11064,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( E @ c_Relation_Osingle__valued ) ) )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1636]) ).
thf(1951,axiom,
tc_Nat_Onat @ class_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(12281,plain,
tc_Nat_Onat @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1951]) ).
thf(4600,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right) ).
thf(22800,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4600]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I1_J) ).
thf(5084,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(1890,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).
thf(12069,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1890]) ).
thf(241,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Otranspose__rel @ ( A @ tc_List_Olist @ tc_List_Olist @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Otranspose ) )
= ( A @ tc_List_Olist @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I1_J) ).
thf(5597,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Otranspose__rel @ ( A @ tc_List_Olist @ tc_List_Olist @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Otranspose ) )
= ( A @ tc_List_Olist @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendR) ).
thf(7290,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1430,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_Oremove1 ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remove1) ).
thf(10189,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_Oremove1 ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(3098,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olistrel1 ) @ ( E @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( E @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).
thf(16924,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olistrel1 ) @ ( E @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( E @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3098]) ).
thf(3544,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(18681,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3544]) ).
thf(3944,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(20285,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3944]) ).
thf(3401,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I6_J) ).
thf(18075,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3401]) ).
thf(80,axiom,
( ( c_Int_OPls @ c_Int_Osucc )
= ( c_Int_OPls @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Pls) ).
thf(5012,plain,
( ( c_Int_OPls @ c_Int_Osucc )
= ( c_Int_OPls @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(5013,plain,
( ( c_Int_OPls @ c_Int_Osucc )
= ( c_Int_OPls @ c_Int_OBit1 ) ),
inference(lifteq,[status(thm)],[5012]) ).
thf(1208,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Divides_OposDivAlg ) @ ( A @ ( B @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__correct) ).
thf(9330,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Divides_OposDivAlg ) @ ( A @ ( B @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(1590,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
thf(10871,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Orev @ hAPP ) )
= ( B @ c_List_Olist_ONil ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__Nil__conv) ).
thf(4857,plain,
! [A: $i,B: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Orev @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ c_List_Orev @ hAPP ) )
= ( B @ c_List_Olist_ONil ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(4266,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OtakeWhile ) ) )
= ( A @ ( D @ ( B @ c_List_OtakeWhile ) ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).
thf(21556,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OtakeWhile ) ) )
= ( A @ ( D @ ( B @ c_List_OtakeWhile ) ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4266]) ).
thf(1528,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(10623,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528]) ).
thf(4414,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Diff) ).
thf(22127,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4414]) ).
thf(3815,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus1__lemma) ).
thf(19776,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3815]) ).
thf(973,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_COMBI @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc) ).
thf(8416,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_COMBI @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(4343,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__diff) ).
thf(21865,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4343]) ).
thf(2954,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( C @ ( G @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( B @ ( tc_HOL_Obool @ ( D @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Set_OCollect @ hAPP ) @ ( F @ c_Finite__Set_Ocard @ hAPP ) )
= A ) )
=> ( ( E @ ( B @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ ( F @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__multicount) ).
thf(16344,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( C @ ( G @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( B @ ( tc_HOL_Obool @ ( D @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Set_OCollect @ hAPP ) @ ( F @ c_Finite__Set_Ocard @ hAPP ) )
= A ) )
=> ( ( E @ ( B @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ ( F @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2954]) ).
thf(2105,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__Int) ).
thf(12828,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2105]) ).
thf(3403,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oremove) ).
thf(18084,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3403]) ).
thf(1529,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).
thf(10626,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) ) ) )
& ( ( ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529]) ).
thf(4471,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
thf(22316,plain,
! [A: $i,B: $i] :
( ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ? [C: $i] : ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ? [C: $i] : ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4471]) ).
thf(2297,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(13647,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2297]) ).
thf(2879,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__listsp__conv__set) ).
thf(16018,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2879]) ).
thf(2493,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Osublist ) ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Osublist ) ) )
= ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__singleton) ).
thf(14495,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Osublist ) ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Osublist ) ) )
= ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2493]) ).
thf(3746,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__0__E) ).
thf(19514,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3746]) ).
thf(2225,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__diff__def) ).
thf(13325,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2225]) ).
thf(2320,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_Relation_ODomain ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__converse) ).
thf(13744,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_Relation_ODomain ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2320]) ).
thf(4277,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I4_J) ).
thf(21601,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4277]) ).
thf(2979,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__trancl) ).
thf(16448,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2979]) ).
thf(3740,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I15_J) ).
thf(19485,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3740]) ).
thf(1184,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
thf(9225,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(3464,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__1) ).
thf(18348,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3464]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Divides_Odivmod__int ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_COMBI @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ ( B @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_COMBI @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_fequal @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_If @ ( tc_Int_Oint @ ( B @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( B @ tc_fun ) @ ( B @ c_COMBB ) ) @ ( tc_Int_Oint @ ( B @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( B @ c_COMBS ) ) @ ( tc_Int_Oint @ ( B @ ( B @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ ( B @ ( B @ c_HOL_OLet ) @ ( tc_Int_Oint @ ( B @ ( B @ ( B @ tc_fun ) @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( B @ ( B @ ( B @ tc_fun ) @ c_COMBB ) ) @ ( tc_Int_Oint @ ( B @ ( tc_Int_Oint @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__num) ).
thf(4820,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Divides_Odivmod__int ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_COMBI @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ ( B @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_COMBI @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_fequal @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_If @ ( tc_Int_Oint @ ( B @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( B @ tc_fun ) @ ( B @ c_COMBB ) ) @ ( tc_Int_Oint @ ( B @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( B @ c_COMBS ) ) @ ( tc_Int_Oint @ ( B @ ( B @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ ( B @ ( B @ c_HOL_OLet ) @ ( tc_Int_Oint @ ( B @ ( B @ ( B @ tc_fun ) @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( B @ ( B @ ( B @ tc_fun ) @ c_COMBB ) ) @ ( tc_Int_Oint @ ( B @ ( tc_Int_Oint @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ tc_fun ) @ ( B @ ( B @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(3318,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanLessThan) ).
thf(17747,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3318]) ).
thf(1078,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus1__odd) ).
thf(8802,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(4133,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( A @ ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__bij__betw__nat__finite__1) ).
thf(21024,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( A @ ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4133]) ).
thf(2215,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
thf(13295,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2215]) ).
thf(4296,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__insert) ).
thf(21677,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4296]) ).
thf(3824,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__subset__iff) ).
thf(19808,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3824]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Oab__semigroup__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( C @ hAPP ) )
= ( G @ ( B @ hAPP ) ) ) )
=> ( ( D @ ( A @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__cong) ).
thf(6523,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Oab__semigroup__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( C @ hAPP ) )
= ( G @ ( B @ hAPP ) ) ) )
=> ( ( D @ ( A @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(854,axiom,
tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Code__Numeral_Oof__nat @ ( c_Code__Numeral_Onat__of @ ( tc_Nat_Onat @ ( tc_Code__Numeral_Ocode__numeral @ c_Typedef_Otype__definition ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition__code__numeral) ).
thf(7986,plain,
tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Code__Numeral_Oof__nat @ ( c_Code__Numeral_Onat__of @ ( tc_Nat_Onat @ ( tc_Code__Numeral_Ocode__numeral @ c_Typedef_Otype__definition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(3674,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastAtMost) ).
thf(19201,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3674]) ).
thf(1759,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_List_Ofoldl ) ) ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__le__sum) ).
thf(11577,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_List_Ofoldl ) ) ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759]) ).
thf(2081,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Union__image) ).
thf(12750,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2081]) ).
thf(2855,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI2) ).
thf(15939,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2855]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsR) ).
thf(7775,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1655,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(11154,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655]) ).
thf(3019,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(16608,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3019]) ).
thf(1108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Enum_Oproduct ) ) ) )
= ( A @ ( B @ ( D @ ( E @ c_Enum_Oproduct ) ) ) @ ( A @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_product_Osimps_I2_J) ).
thf(8929,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Enum_Oproduct ) ) ) )
= ( A @ ( B @ ( D @ ( E @ c_Enum_Oproduct ) ) ) @ ( A @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(3240,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I9_J) ).
thf(17453,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3240]) ).
thf(1334,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
thf(9811,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(4652,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).
thf(23011,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4652]) ).
thf(4618,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(22870,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4618]) ).
thf(3283,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
thf(17630,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3283]) ).
thf(3364,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq2) ).
thf(17916,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3364]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_List_OtakeWhile ) ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__takeWhile__less__P__nth) ).
thf(7845,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_List_OtakeWhile ) ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__collapse) ).
thf(7926,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(4217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
thf(21352,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4217]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( C @ ( A @ c_Hilbert__Choice_OEps ) @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI) ).
thf(6176,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( C @ ( A @ c_Hilbert__Choice_OEps ) @ ( C @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(4206,axiom,
( ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__lessThan__UNIV) ).
thf(21322,plain,
( ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4206]) ).
thf(868,axiom,
tc_Int_Oint @ class_Rings_Odvd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
thf(8065,plain,
tc_Int_Oint @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(2651,axiom,
! [A: $i] :
( ( A @ class_Orderings_Owellorder )
=> ( A @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( A @ ( A @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( A @ ( A @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf) ).
thf(15150,plain,
! [A: $i] :
( ( A @ class_Orderings_Owellorder )
=> ( A @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( A @ ( A @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( A @ ( A @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2651]) ).
thf(4054,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oeq__fold_H) ).
thf(20655,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4054]) ).
thf(1831,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
thf(11838,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1831]) ).
thf(3224,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__nonneg) ).
thf(17398,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3224]) ).
thf(3040,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__Compl__image__subset) ).
thf(16693,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3040]) ).
thf(1571,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__insert) ).
thf(10816,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571]) ).
thf(1992,axiom,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( A @ ( B @ c_Complete__Lattice_OSup__class_OSup ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin__Sup) ).
thf(12436,plain,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( A @ ( B @ c_Complete__Lattice_OSup__class_OSup ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1992]) ).
thf(1928,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).
thf(12204,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1928]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oconcat ) @ ( B @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_List_Orev @ hAPP ) @ ( B @ c_List_Orev @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Oconcat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__concat) ).
thf(5541,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oconcat ) @ ( B @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_List_Orev @ hAPP ) @ ( B @ c_List_Orev @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Oconcat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(3246,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(17485,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3246]) ).
thf(2943,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseD) ).
thf(16293,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2943]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(5156,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(2045,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__1) ).
thf(12625,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2045]) ).
thf(3594,axiom,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus1__eq__if) ).
thf(18889,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3594]) ).
thf(2758,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Groups_Ocomm__monoid__add )
=> ( ( E @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( G @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( F @ ( G @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( G @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_HOL_Obool @ ( D @ ( F @ c_COMBC ) ) @ hAPP ) @ ( E @ ( F @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Set_OCollect @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( G @ ( D @ ( F @ c_COMBC ) ) @ hAPP ) @ ( G @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( D @ ( G @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ tc_fun ) @ ( G @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__setsum__restrict) ).
thf(15554,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Groups_Ocomm__monoid__add )
=> ( ( E @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( G @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( F @ ( G @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( G @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_HOL_Obool @ ( D @ ( F @ c_COMBC ) ) @ hAPP ) @ ( E @ ( F @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Set_OCollect @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( G @ ( D @ ( F @ c_COMBC ) ) @ hAPP ) @ ( G @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( D @ ( G @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ tc_fun ) @ ( G @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2758]) ).
thf(365,axiom,
tc_HOL_Obool @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(6054,plain,
tc_HOL_Obool @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(2984,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( E @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).
thf(16476,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( E @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2984]) ).
thf(1719,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__iff__zadd) ).
thf(11398,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I14_J) ).
thf(7015,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(4509,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= A ) )
& ( ( D
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__constant) ).
thf(22456,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= A ) )
& ( ( D
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4509]) ).
thf(4468,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert) ).
thf(22307,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4468]) ).
thf(4189,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).
thf(21261,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4189]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(5805,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(1291,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__nth__monoI) ).
thf(9680,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(3119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI2) ).
thf(16989,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3119]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onat__gcd__rel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Nitpick_Onat__gcd ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_Nitpick_Onat__gcd ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Nitpick_Onat__gcd ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Opsimps) ).
thf(4871,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onat__gcd__rel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Nitpick_Onat__gcd ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_Nitpick_Onat__gcd ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Nitpick_Onat__gcd ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
thf(8246,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Divides_OnegDivAlg ) @ ( A @ ( B @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__correct) ).
thf(5135,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Divides_OnegDivAlg ) @ ( A @ ( B @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(1798,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Otl @ hAPP ) @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__tl) ).
thf(11708,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Otl @ hAPP ) @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1798]) ).
thf(4472,axiom,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
thf(22325,plain,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4472]) ).
thf(1468,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Enum_On__lists ) ) @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__n__lists) ).
thf(10378,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Enum_On__lists ) ) @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ ( D @ c_Groups_Otimes__class_Otimes @ ( tc_Nat_Onat @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ ( tc_Nat_Onat @ ( D @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__general) ).
thf(5761,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ ( D @ c_Groups_Otimes__class_Otimes @ ( tc_Nat_Onat @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ ( tc_Nat_Onat @ ( D @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(2434,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__I) ).
thf(14238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2434]) ).
thf(1866,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I47_J) ).
thf(11971,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1866]) ).
thf(3634,axiom,
( ( tc_Nat_Onat @ c_Lattices_Osemilattice__inf__class_Oinf )
= ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__nat__def) ).
thf(19056,plain,
( ( tc_Nat_Onat @ c_Lattices_Osemilattice__inf__class_Oinf )
= ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3634]) ).
thf(447,axiom,
! [A: $i] : ( A @ c_Relation_OId @ ( A @ c_Relation_Osym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Id) ).
thf(6438,plain,
! [A: $i] : ( A @ c_Relation_OId @ ( A @ c_Relation_Osym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(622,axiom,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(7139,plain,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(2287,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(13604,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2287]) ).
thf(3387,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq__iff) ).
thf(18026,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( ( ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) ) ) )
=> ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3387]) ).
thf(3209,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__fin__set__fold) ).
thf(17342,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3209]) ).
thf(1840,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__Suc__eq__div__add3) ).
thf(11870,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1840]) ).
thf(3809,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf__absorb) ).
thf(19759,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3809]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__of__int) ).
thf(4783,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1882,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).
thf(12041,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1882]) ).
thf(1324,axiom,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__power2) ).
thf(9779,plain,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(3565,axiom,
( ( c_Com_Ocom_OSKIP @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I9_J) ).
thf(18786,plain,
( ( c_Com_Ocom_OSKIP @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3565]) ).
thf(3793,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( D @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ ( E @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).
thf(19700,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( D @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ ( E @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3793]) ).
thf(3515,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I4_J) ).
thf(18560,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3515]) ).
thf(3091,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= A )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__eq) ).
thf(16897,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= A )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3091]) ).
thf(311,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__upt) ).
thf(5834,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(1746,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).
thf(11523,plain,
tc_Code__Numeral_Ocode__numeral @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746]) ).
thf(3434,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion__inter) ).
thf(18241,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3434]) ).
thf(2809,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterD) ).
thf(15738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2809]) ).
thf(89,axiom,
tc_Int_Oint @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(5045,plain,
tc_Int_Oint @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(3799,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Orderings_Olinorder )
& ( C @ class_Complete__Lattice_Ocomplete__lattice ) )
=> ( ( A @ ( B @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i] :
( ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__less__iff) ).
thf(19717,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Orderings_Olinorder )
& ( C @ class_Complete__Lattice_Ocomplete__lattice ) )
=> ( ( ? [D: $i] :
( ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3799]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_List_Olenlex ) @ ( B @ tc_List_Olist @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lenlex) ).
thf(5059,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_List_Olenlex ) @ ( B @ tc_List_Olist @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(3546,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield__inverse__zero )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__dividef) ).
thf(18693,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield__inverse__zero )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3546]) ).
thf(4577,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Opos__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Opos__single ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__single__def) ).
thf(22713,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Opos__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Opos__single ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4577]) ).
thf(1351,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ ( E @ c_Relation_Osingle__valued ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( B @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__eq) ).
thf(9875,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ ( E @ c_Relation_Osingle__valued ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( B @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(1621,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ c_Nat__Transfer_Otsub ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).
thf(11004,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ c_Nat__Transfer_Otsub ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621]) ).
thf(2995,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( D @ ( F @ c_Groups_Oone__class_Oone @ ( B @ ( F @ c_Groups_Oone__class_Oone @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ ( C @ ( F @ c_Finite__Set_Ofold__image ) ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( F @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( C @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oone__class_Oone @ ( A @ ( F @ ( C @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ ( C @ ( E @ tc_prod ) @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Sigma) ).
thf(16527,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( D @ ( F @ c_Groups_Oone__class_Oone @ ( B @ ( F @ c_Groups_Oone__class_Oone @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ ( C @ ( F @ c_Finite__Set_Ofold__image ) ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( F @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( C @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oone__class_Oone @ ( A @ ( F @ ( C @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ ( C @ ( E @ tc_prod ) @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2995]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__of__nat__eq) ).
thf(4749,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4750,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
| ~ ( B @ class_Rings_Oring__1 ) ),
inference(cnf,[status(esa)],[4749]) ).
thf(4751,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Rings_Oring__1 )
| ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4750]) ).
thf(2708,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_OImage ) ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton) ).
thf(15365,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_OImage ) ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2708]) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__neg__trivial) ).
thf(5738,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(932,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( A @ ( A @ ( B @ hAPP ) @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__same) ).
thf(8274,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( A @ ( A @ ( B @ hAPP ) @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(1737,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Lazy__Sequence_Osmall__lazy_H__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) @ ( A @ ( tc_Int_Oint @ c_Lazy__Sequence_Osingle @ hAPP ) @ ( tc_Int_Oint @ c_Lazy__Sequence_Oappend ) ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) )
= ( tc_Int_Oint @ c_Lazy__Sequence_Oempty ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__lazy_H_Opsimps) ).
thf(11480,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Lazy__Sequence_Osmall__lazy_H__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) @ ( A @ ( tc_Int_Oint @ c_Lazy__Sequence_Osingle @ hAPP ) @ ( tc_Int_Oint @ c_Lazy__Sequence_Oappend ) ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) )
= ( tc_Int_Oint @ c_Lazy__Sequence_Oempty ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737]) ).
thf(1736,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).
thf(11478,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736]) ).
thf(1696,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
<=> ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__key) ).
thf(11312,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) ) )
& ( ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696]) ).
thf(1359,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Omeasures ) )
= ( A @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_COMBI @ ( tc_Nat_Onat @ ( B @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Omap ) @ ( B @ ( tc_Nat_Onat @ tc_List_Olist @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ tc_List_Olist @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ c_List_Olex ) @ ( B @ ( tc_Nat_Onat @ tc_List_Olist @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__def) ).
thf(9897,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Omeasures ) )
= ( A @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_COMBI @ ( tc_Nat_Onat @ ( B @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Omap ) @ ( B @ ( tc_Nat_Onat @ tc_List_Olist @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ tc_List_Olist @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ c_List_Olex ) @ ( B @ ( tc_Nat_Onat @ tc_List_Olist @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(4549,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
thf(22610,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4549]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__append) ).
thf(5773,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(3765,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc__Suc) ).
thf(19591,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3765]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1) ).
thf(6451,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(4474,axiom,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__empty) ).
thf(22329,plain,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4474]) ).
thf(2658,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ohom__commute) ).
thf(15186,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2658]) ).
thf(4109,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(20934,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4109]) ).
thf(2500,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Wellfounded_Ofinite__psubset @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
thf(14527,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ c_Wellfounded_Ofinite__psubset @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ c_Wellfounded_Ofinite__psubset @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2500]) ).
thf(3087,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( C @ ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( G @ tc_fun ) @ ( H @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( A @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( E @ ( A @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__E) ).
thf(16885,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( C @ ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( G @ tc_fun ) @ ( H @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( A @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( E @ ( A @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3087]) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Code__Numeral_OSuc__code__numeral )
= ( A @ c_Code__Numeral_OSuc__code__numeral ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Oinject) ).
thf(5401,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Code__Numeral_OSuc__code__numeral )
= ( A @ c_Code__Numeral_OSuc__code__numeral ) ) )
& ( ( ( B @ c_Code__Numeral_OSuc__code__numeral )
= ( A @ c_Code__Numeral_OSuc__code__numeral ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(2218,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oinsert) ).
thf(13305,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2218]) ).
thf(745,axiom,
tc_Int_Oint @ class_Lattices_Osemilattice__sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__sup) ).
thf(7613,plain,
tc_Int_Oint @ class_Lattices_Osemilattice__sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(3079,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( B @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( L @ ( K @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( E @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
thf(16841,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( B @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( L @ ( K @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( E @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3079]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_COMBI @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Bit0) ).
thf(4842,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_COMBI @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_COMBI @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__even__number__of) ).
thf(5210,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_COMBI @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(2052,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_List_Olists ) )
= ( tc_HOL_Obool @ ( A @ tc_List_Olist @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__UNIV) ).
thf(12653,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_List_Olists ) )
= ( tc_HOL_Obool @ ( A @ tc_List_Olist @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2052]) ).
thf(4257,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(21525,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4257]) ).
thf(2849,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(15907,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2849]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odvd )
=> ( ( C
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvdI) ).
thf(8774,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odvd )
=> ( ( C
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(3642,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__partition) ).
thf(19084,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3642]) ).
thf(3768,axiom,
! [A: $i,B: $i] :
( ( c_Int_OInteg @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i] : ( C @ ( c_Int_ORep__Integ @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__induct) ).
thf(19608,plain,
! [A: $i,B: $i] :
( ( c_Int_OInteg @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i] : ( C @ ( c_Int_ORep__Integ @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3768]) ).
thf(1123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
thf(8977,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(528,axiom,
! [A: $i] :
( ( ( A
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( c_Code__Numeral_Oint__of @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oint__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( c_Code__Numeral_Oint__of @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oint__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( A
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( c_Code__Numeral_Oint__of @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__of__code) ).
thf(6777,plain,
! [A: $i] :
( ( ( A
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( c_Code__Numeral_Oint__of @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oint__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( c_Code__Numeral_Oint__of @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oint__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( A
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( c_Code__Numeral_Oint__of @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(1019,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
thf(8575,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(2956,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).
thf(16357,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2956]) ).
thf(3668,axiom,
! [A: $i,B: $i] : ( A @ ( B @ tc_sum ) @ class_Nat_Osize ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Nat_Osize) ).
thf(19177,plain,
! [A: $i,B: $i] : ( A @ ( B @ tc_sum ) @ class_Nat_Osize ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3668]) ).
thf(1170,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oassoc) ).
thf(9167,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(3970,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ hAPP ) )
= ( A @ ( D @ ( C @ tc_fun ) @ c_COMBI @ ( D @ ( C @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_fun ) @ c_HOL_OEx @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Complete__Lattice_OSup__class_OSup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__apply) ).
thf(20368,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ hAPP ) )
= ( A @ ( D @ ( C @ tc_fun ) @ c_COMBI @ ( D @ ( C @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( D @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_fun ) @ c_HOL_OEx @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Complete__Lattice_OSup__class_OSup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3970]) ).
thf(4491,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) )
<=> ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__is__image) ).
thf(22385,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4491]) ).
thf(3297,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( D @ c_List_Oset__Cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons) ).
thf(17674,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( D @ c_List_Oset__Cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3297]) ).
thf(3287,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
thf(17645,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3287]) ).
thf(2089,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(12777,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2089]) ).
thf(1082,axiom,
tc_Int_Oint @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
thf(8817,plain,
tc_Int_Oint @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(1310,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(9743,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(3211,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I2_J) ).
thf(17349,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3211]) ).
thf(3523,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Set_OPow @ hAPP ) @ ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( C @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Pow__subset) ).
thf(18578,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Set_OPow @ hAPP ) @ ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( C @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3523]) ).
thf(2411,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) )
<=> ( ( C = A )
& ( D = B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
thf(14113,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2411]) ).
thf(3530,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__ConsD) ).
thf(18604,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3530]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(6947,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(829,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).
thf(7909,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(4300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ! [E: $i] :
( ( E @ ( C @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( tc_HOL_Obool @ ( D @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__bounded__ex) ).
thf(21694,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ! [E: $i] :
( ( E @ ( C @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( tc_HOL_Obool @ ( D @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( E @ ( C @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( tc_HOL_Obool @ ( D @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4300]) ).
thf(1874,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oin__idem) ).
thf(12008,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1874]) ).
thf(3579,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
thf(18842,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3579]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
thf(4996,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1474,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(10405,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__r__diff__Id) ).
thf(6932,plain,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(2170,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
<=> ? [F: $i,G: $i] :
( ~ ( G @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( G @ ( F @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
& ( ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set_Oequations) ).
thf(13106,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i,G: $i] :
( ~ ( G @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( G @ ( F @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
& ( ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
=> ( A @ ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
=> ? [F: $i,G: $i] :
( ~ ( G @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( G @ ( F @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
& ( ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2170]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ c_Code__Numeral_OSuc__code__numeral )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__code__numeral__def) ).
thf(5246,plain,
! [A: $i] :
( ( A @ c_Code__Numeral_OSuc__code__numeral )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(3901,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
thf(20130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3901]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).
thf(8347,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
thf(5846,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(1561,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).
thf(10784,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).
thf(3717,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(19379,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3717]) ).
thf(3606,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i,H: $i] :
( ( C
= ( H @ ( E @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( G @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( B
!= ( H @ ( F @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( G @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1E) ).
thf(18930,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i,H: $i] :
( ( C
= ( H @ ( E @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( G @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( B
!= ( H @ ( F @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( G @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3606]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod) ).
thf(7194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__power) ).
thf(5169,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(2009,axiom,
tc_HOL_Obool @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
thf(12499,plain,
tc_HOL_Obool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2009]) ).
thf(2269,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olistrel ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__mono) ).
thf(13521,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olistrel ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2269]) ).
thf(4458,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
thf(22271,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4458]) ).
thf(3912,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__mono) ).
thf(20174,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3912]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__append) ).
thf(5897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(3783,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( E @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [F: $i] :
( ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__INF__iff) ).
thf(19661,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( ! [F: $i] :
( ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3783]) ).
thf(1844,axiom,
! [A: $i] :
( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Opred @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__diff__1) ).
thf(11885,plain,
! [A: $i] :
( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Opred @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1844]) ).
thf(3005,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Odistrib__lattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib2) ).
thf(16562,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Odistrib__lattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3005]) ).
thf(4255,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
thf(21520,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4255]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__power) ).
thf(8459,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(3461,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( D @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
!= ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I3_J) ).
thf(18329,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( D @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
!= ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3461]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ c_List_OtakeWhile ) ) @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Osnd ) @ ( B @ ( D @ ( E @ tc_prod ) @ ( tc_HOL_Obool @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_OtakeWhile ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__takeWhile__snd) ).
thf(6021,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ c_List_OtakeWhile ) ) @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Osnd ) @ ( B @ ( D @ ( E @ tc_prod ) @ ( tc_HOL_Obool @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_OtakeWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(898,axiom,
tc_Nat_Onat @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(8173,plain,
tc_Nat_Onat @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(1410,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted__list__of__set ) )
= ( A @ ( B @ c_List_Oupt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__range) ).
thf(10106,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted__list__of__set ) )
= ( A @ ( B @ c_List_Oupt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).
thf(1221,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_List_Oupt ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
<=> ( ( ( C @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupt ) )
= A )
& ( D = B )
& ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__eq__Cons__conv) ).
thf(9368,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( C @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupt ) )
= A )
& ( D = B )
& ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( D @ c_List_Oupt ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ c_List_Oupt ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( ( C @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupt ) )
= A )
& ( D = B )
& ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(1260,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).
thf(9533,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(3010,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__le__fold__sup) ).
thf(16577,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3010]) ).
thf(1214,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_OposDivAlg ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__div__mod) ).
thf(9347,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_OposDivAlg ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(4170,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(21168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4170]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ c_Nitpick_Onat__gcd ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Nitpick_Onat__gcd ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ c_Nitpick_Onat__gcd ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Osimps) ).
thf(5489,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ c_Nitpick_Onat__gcd ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Nitpick_Onat__gcd ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ c_Nitpick_Onat__gcd ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(3453,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(18296,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3453]) ).
thf(2414,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__compl__bot) ).
thf(14128,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2414]) ).
thf(677,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Orderings_Olinorder )
=> ( ( ( D @ ( E @ hAPP ) )
!= ( C @ ( E @ hAPP ) ) )
=> ( ( A @ ( D @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key__left__comm) ).
thf(7337,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Orderings_Olinorder )
=> ( ( ( D @ ( E @ hAPP ) )
!= ( C @ ( E @ hAPP ) ) )
=> ( ( A @ ( D @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(23813,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( C @ ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4741,4729]) ).
thf(23878,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= C )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23813]) ).
thf(23909,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23878]) ).
thf(1097,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ c_Int_Osucc @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__number__of__add) ).
thf(8892,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ c_Int_Osucc @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(3312,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Osemilattice__sup )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__mono) ).
thf(17719,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Osemilattice__sup )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3312]) ).
thf(2138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).
thf(12966,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2138]) ).
thf(114,axiom,
tc_Nat_Onat @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
thf(5137,plain,
tc_Nat_Onat @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(3015,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(16594,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3015]) ).
thf(1012,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
thf(8554,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(4592,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Relation_OField @ hAPP ) )
= ( A @ ( D @ c_Relation_OField @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__insert) ).
thf(22774,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Relation_OField @ hAPP ) )
= ( A @ ( D @ c_Relation_OField @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4592]) ).
thf(1130,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__idem) ).
thf(9007,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(600,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oremdups ) @ ( B @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remdups) ).
thf(7051,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oremdups ) @ ( B @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(717,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).
thf(7505,plain,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(3775,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( D @ c_Finite__Set_Ocard @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
thf(19629,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( D @ c_Finite__Set_Ocard @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3775]) ).
thf(4263,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oeq__fold) ).
thf(21542,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4263]) ).
thf(4102,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
thf(20905,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4102]) ).
thf(1603,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(10933,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603]) ).
thf(3082,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(16858,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3082]) ).
thf(2553,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb1) ).
thf(14761,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2553]) ).
thf(4534,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Set_OPow @ hAPP ) )
= ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( C @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__Int__eq) ).
thf(22556,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Set_OPow @ hAPP ) )
= ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( C @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4534]) ).
thf(958,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Nil) ).
thf(8362,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(4569,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ! [C: $i] :
~ ( C @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
thf(22685,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( C @ ( A @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ! [C: $i] :
~ ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4569]) ).
thf(4154,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).
thf(21107,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4154]) ).
thf(2363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI1) ).
thf(13891,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2363]) ).
thf(4327,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
thf(21816,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4327]) ).
thf(3199,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
thf(17298,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3199]) ).
thf(4368,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( A @ ( B @ ( C @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__sound) ).
thf(21972,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( A @ ( B @ ( C @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4368]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__int) ).
thf(5970,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(4488,axiom,
! [A: $i] : ( A @ tc_Hoare__Mirabelle_Otriple @ class_Nat_Osize ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).
thf(22377,plain,
! [A: $i] : ( A @ tc_Hoare__Mirabelle_Otriple @ class_Nat_Osize ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4488]) ).
thf(22378,plain,
! [A: $i] : ( A @ tc_Hoare__Mirabelle_Otriple @ class_Nat_Osize ),
inference(cnf,[status(esa)],[22377]) ).
thf(2120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Equiv__Relations_Ocongruent ) ) ) )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [H: $i] :
( ( F @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( H @ ( C @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__type) ).
thf(12892,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Equiv__Relations_Ocongruent ) ) ) )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [H: $i] :
( ( F @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( H @ ( C @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2120]) ).
thf(1413,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I28_J) ).
thf(10113,plain,
! [A: $i] :
( ( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(548,axiom,
! [A: $i,B: $i] :
( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).
thf(6860,plain,
! [A: $i,B: $i] :
( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(4080,axiom,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(20781,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4080]) ).
thf(3531,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( E
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__remainder) ).
thf(18607,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( E
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3531]) ).
thf(3006,axiom,
( ( c_fFalse @ ( tc_HOL_Obool @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I4_J) ).
thf(16565,plain,
( ( c_fFalse @ ( tc_HOL_Obool @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3006]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ ( G @ ( E @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) @ ( F @ ( G @ c_Product__Type_Osnd ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__prod__fun) ).
thf(8289,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ ( G @ ( E @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) @ ( F @ ( G @ c_Product__Type_Osnd ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(2085,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Osym ) )
=> ( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( A @ ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__trans__comp__subset) ).
thf(12762,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Osym ) )
=> ( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( A @ ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2085]) ).
thf(3825,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atMost) ).
thf(19812,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3825]) ).
thf(1106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) @ ( A @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).
thf(8924,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) @ ( A @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(3391,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D
= ( B @ ( G @ ( H @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( H @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( A
= ( B @ ( F @ ( H @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( H @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( E @ ( H @ c_List_Olistrel1 ) @ ( A @ ( D @ ( H @ tc_List_Olist @ ( H @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ tc_List_Olist @ ( H @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I) ).
thf(18047,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D
= ( B @ ( G @ ( H @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( H @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( A
= ( B @ ( F @ ( H @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( H @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( E @ ( H @ c_List_Olistrel1 ) @ ( A @ ( D @ ( H @ tc_List_Olist @ ( H @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ tc_List_Olist @ ( H @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3391]) ).
thf(3479,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Osublist ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Onth @ hAPP ) @ ( c_fequal @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sublist) ).
thf(18412,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Osublist ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Onth @ hAPP ) @ ( c_fequal @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3479]) ).
thf(2899,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).
thf(16109,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2899]) ).
thf(3514,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(18550,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3514]) ).
thf(1538,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).
thf(10690,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).
thf(1783,axiom,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).
thf(11660,plain,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783]) ).
thf(4312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D != C )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OremoveAll ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_OremoveAll ) @ hAPP ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( D = C )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OremoveAll ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_OremoveAll ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll_Osimps_I2_J) ).
thf(21736,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D != C )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OremoveAll ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_OremoveAll ) @ hAPP ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( D = C )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OremoveAll ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_OremoveAll ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4312]) ).
thf(3402,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectE) ).
thf(18081,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3402]) ).
thf(1789,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__apply) ).
thf(11677,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789]) ).
thf(4093,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__pos__if__in__set) ).
thf(20836,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4093]) ).
thf(4620,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(22877,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4620]) ).
thf(1762,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_List_Oupto ) @ ( C @ ( D @ ( tc_Int_Oint @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).
thf(11597,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_List_Oupto ) @ ( C @ ( D @ ( tc_Int_Oint @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762]) ).
thf(1559,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__less) ).
thf(10779,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1559]) ).
thf(2509,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(14569,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2509]) ).
thf(1497,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__append__eq) ).
thf(10494,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ ( E @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Nat_Onat_Onat__case ) ) ) @ ( c_Nat__Numeral_Oneg @ ( E @ c_If @ ( tc_Int_Oint @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( E @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__add__eq__if) ).
thf(7674,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ ( E @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Nat_Onat_Onat__case ) ) ) @ ( c_Nat__Numeral_Oneg @ ( E @ c_If @ ( tc_Int_Oint @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( E @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(1657,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__int__eq) ).
thf(11159,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657]) ).
thf(2621,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I14_J) ).
thf(15046,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2621]) ).
thf(3909,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Groups_Ocomm__monoid__mult )
& ( E @ class_Groups_Ocomm__monoid__add ) )
=> ( ( D = C )
=> ( ( C @ c_Nat__Transfer_Onat__set )
=> ( ! [F: $i] :
( ( F @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) )
=> ( ( D @ ( B @ ( E @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).
thf(20157,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Groups_Ocomm__monoid__mult )
& ( E @ class_Groups_Ocomm__monoid__add ) )
=> ( ( D = C )
=> ( ( C @ c_Nat__Transfer_Onat__set )
=> ( ! [F: $i] :
( ( F @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) )
=> ( ( D @ ( B @ ( E @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3909]) ).
thf(641,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I3_J) ).
thf(7197,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1399,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).
thf(10062,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(3836,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__inf__le) ).
thf(19877,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3836]) ).
thf(1303,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OnegDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OnegDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Opinduct) ).
thf(9720,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OnegDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OnegDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(2361,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
thf(13885,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2361]) ).
thf(654,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__trans) ).
thf(7254,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(1836,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
thf(11852,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1836]) ).
thf(1650,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ ( C @ ( E @ ( F @ tc_prod ) @ ( E @ c_COMBB ) ) @ ( F @ ( E @ ( F @ tc_prod ) @ ( C @ tc_fun ) @ ( E @ ( C @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ ( C @ tc_fun ) @ ( E @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ ( C @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ ( C @ ( F @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map2) ).
thf(11121,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ ( C @ ( E @ ( F @ tc_prod ) @ ( E @ c_COMBB ) ) @ ( F @ ( E @ ( F @ tc_prod ) @ ( C @ tc_fun ) @ ( E @ ( C @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ ( C @ tc_fun ) @ ( E @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ ( C @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ ( C @ ( F @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650]) ).
thf(3554,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Relation_OField @ hAPP ) )
= ( A @ ( C @ c_Relation_OField @ hAPP ) @ ( B @ ( C @ c_Relation_OField @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Un) ).
thf(18742,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Relation_OField @ hAPP ) )
= ( A @ ( C @ c_Relation_OField @ hAPP ) @ ( B @ ( C @ c_Relation_OField @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3554]) ).
thf(3231,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).
thf(17423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3231]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2) ).
thf(6529,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(2502,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(14537,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2502]) ).
thf(993,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Obutlast ) @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__butlast) ).
thf(8486,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Obutlast ) @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(815,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( F @ ( G @ ( H @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( G @ ( E @ ( H @ ( A @ ( B @ ( C @ c_Predicate_Opred__comp ) ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
thf(7849,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( F @ ( G @ ( H @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( G @ ( E @ ( H @ ( A @ ( B @ ( C @ c_Predicate_Opred__comp ) ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(4176,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__upto) ).
thf(21202,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4176]) ).
thf(3488,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
<=> ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(18445,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3488]) ).
thf(1127,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self4) ).
thf(8999,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(1569,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield__inverse__zero ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus1__divide) ).
thf(10811,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield__inverse__zero ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569]) ).
thf(2238,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oinsert__idem) ).
thf(13386,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2238]) ).
thf(2229,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ ( F @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__apply) ).
thf(13337,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ ( F @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2229]) ).
thf(3004,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(16560,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3004]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__filter) ).
thf(8655,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(4379,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
=> ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__nonempty) ).
thf(22011,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
=> ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4379]) ).
thf(4460,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton) ).
thf(22282,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4460]) ).
thf(2037,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omax__weak @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmax__emptyI) ).
thf(12586,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omax__weak @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2037]) ).
thf(2571,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__imp__inj__on) ).
thf(14836,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2571]) ).
thf(1685,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(11255,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Enum_On__lists ) ) @ ( D @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__n__lists__elem) ).
thf(8046,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Enum_On__lists ) ) @ ( D @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(1718,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_Hilbert__Choice_OEps ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
thf(11395,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_Hilbert__Choice_OEps ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718]) ).
thf(1950,axiom,
! [A: $i] :
( ( A @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__def) ).
thf(12275,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1950]) ).
thf(1107,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__2__gt__zero) ).
thf(8927,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(1151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( C @ c_List_Olist_ONil ) )
=> ( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olast ) )
= ( D @ ( C @ c_List_Olast ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olast ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__list__update) ).
thf(9090,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( C @ c_List_Olist_ONil ) )
=> ( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olast ) )
= ( D @ ( C @ c_List_Olast ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olast ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oreplicate ) ) @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__replicate) ).
thf(4888,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oreplicate ) ) @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(5839,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(2786,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( C @ ( G @ ( D @ ( H @ ( E @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( G @ ( H @ tc_prod ) @ ( D @ ( E @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( G @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [I: $i,J: $i] :
( ( F
= ( J @ ( B @ hAPP ) @ ( I @ ( C @ hAPP ) @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( J @ ( I @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__fun__imageE) ).
thf(15655,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( C @ ( G @ ( D @ ( H @ ( E @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( G @ ( H @ tc_prod ) @ ( D @ ( E @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( G @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [I: $i,J: $i] :
( ( F
= ( J @ ( B @ hAPP ) @ ( I @ ( C @ hAPP ) @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( J @ ( I @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2786]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__minus1) ).
thf(5411,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(4053,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_ODomain ) @ hAPP ) )
= ( A @ ( B @ ( B @ c_Relation_ODomain ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__domain) ).
thf(20652,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_ODomain ) @ hAPP ) )
= ( A @ ( B @ ( B @ c_Relation_ODomain ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4053]) ).
thf(3413,axiom,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL )
<=> ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_enum__all) ).
thf(18145,plain,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL )
=> ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3413]) ).
thf(3924,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__pred__less) ).
thf(20216,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3924]) ).
thf(776,axiom,
! [A: $i] :
( ( A @ c_List_Omember )
= ( A @ c_List_Oset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_member__set) ).
thf(7725,plain,
! [A: $i] :
( ( A @ c_List_Omember )
= ( A @ c_List_Oset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(3457,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(18312,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3457]) ).
thf(1514,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(10561,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).
thf(3872,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(20025,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3872]) ).
thf(920,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Ofilter ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter_Osimps_I1_J) ).
thf(8243,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Ofilter ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(2859,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( A @ ( B @ ( D @ ( C @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__subset) ).
thf(15952,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( A @ ( B @ ( D @ ( C @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2859]) ).
thf(1158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).
thf(9136,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
thf(6047,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1998,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc) ).
thf(12457,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1998]) ).
thf(2901,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__in) ).
thf(16119,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2901]) ).
thf(1500,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Oreplicate ) ) @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( D @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__replicate) ).
thf(10506,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Oreplicate ) ) @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( D @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).
thf(1337,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(9836,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(3222,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(17389,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3222]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Otrans ) )
=> ( A @ ( C @ ( B @ ( D @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__inv__image) ).
thf(7814,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Otrans ) )
=> ( A @ ( C @ ( B @ ( D @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(2471,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
<=> ! [C: $i] :
~ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
thf(14420,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) )
& ( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ! [C: $i] :
~ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2471]) ).
thf(1129,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp__self__comp) ).
thf(9004,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(2560,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( E @ ( H @ ( G @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [I: $i,J: $i] :
( ( C @ ( J @ ( I @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( G @ ( B @ hAPP ) @ hAPP ) )
= ( J @ ( H @ ( B @ hAPP ) @ hAPP ) ) ) ) )
=> ( B @ ( C @ ( E @ ( A @ ( D @ ( F @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2I_H) ).
thf(14785,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( E @ ( H @ ( G @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [I: $i,J: $i] :
( ( C @ ( J @ ( I @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( G @ ( B @ hAPP ) @ hAPP ) )
= ( J @ ( H @ ( B @ hAPP ) @ hAPP ) ) ) ) )
=> ( B @ ( C @ ( E @ ( A @ ( D @ ( F @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2560]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zmod) ).
thf(8365,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(7037,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Ofoldr ) ) ) ) )
= ( B @ ( E @ c_List_Orev @ hAPP ) @ ( A @ ( C @ ( D @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ ( E @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__foldl) ).
thf(5017,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Ofoldr ) ) ) ) )
= ( B @ ( E @ c_List_Orev @ hAPP ) @ ( A @ ( C @ ( D @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ ( E @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(2310,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).
thf(13709,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2310]) ).
thf(3411,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicI) ).
thf(18140,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3411]) ).
thf(965,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__idem) ).
thf(8382,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(1659,axiom,
! [A: $i] :
( ( A @ class_Lattices_Osemilattice__sup )
=> ( A @ c_Lattices_Osemilattice__sup__class_Osup @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__sup) ).
thf(11170,plain,
! [A: $i] :
( ( A @ class_Lattices_Osemilattice__sup )
=> ( A @ c_Lattices_Osemilattice__sup__class_Osup @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( C @ ( D @ c_List_Orev @ hAPP ) @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_List_Orev @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__rev) ).
thf(5438,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( C @ ( D @ c_List_Orev @ hAPP ) @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_List_Orev @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(384,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
thf(6139,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(2726,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).
thf(15424,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2726]) ).
thf(1995,axiom,
! [A: $i] : ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zless__0) ).
thf(12446,plain,
! [A: $i] : ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1995]) ).
thf(3540,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(18658,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3540]) ).
thf(4573,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( c_fFalse @ ( A @ ( tc_HOL_Obool @ c_COMBK ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
thf(22701,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( c_fFalse @ ( A @ ( tc_HOL_Obool @ c_COMBK ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4573]) ).
thf(1076,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__le__iff) ).
thf(8795,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(4631,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(22916,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4631]) ).
thf(2444,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__finite__eq) ).
thf(14295,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2444]) ).
thf(825,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Ohd @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__conv__nth) ).
thf(7885,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Ohd @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I37_J) ).
thf(5070,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(2127,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(12927,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2127]) ).
thf(3978,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Odistrib__sup__le) ).
thf(20395,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3978]) ).
thf(1086,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__eq__minus1) ).
thf(8827,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(1787,axiom,
( c_Code__Numeral_Oint__of
= ( c_Code__Numeral_Onat__of @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__of__def) ).
thf(11672,plain,
( c_Code__Numeral_Oint__of
= ( c_Code__Numeral_Onat__of @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787]) ).
thf(3817,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ) )
& ( ( D
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons_H) ).
thf(19781,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ) )
& ( ( D
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3817]) ).
thf(2454,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(14342,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2454]) ).
thf(4256,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__absorb) ).
thf(21522,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4256]) ).
thf(2866,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fdisj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__def) ).
thf(15979,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fdisj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2866]) ).
thf(3050,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
thf(16736,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3050]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Osublist ) ) )
= ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ ( C @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( C @ c_Product__Type_Osnd ) @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( C @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( C @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( C @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ ( C @ c_Product__Type_Ofst ) @ ( C @ ( tc_Nat_Onat @ ( C @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__def) ).
thf(7269,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Osublist ) ) )
= ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ ( C @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( C @ c_Product__Type_Osnd ) @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( C @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( C @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( C @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ ( C @ c_Product__Type_Ofst ) @ ( C @ ( tc_Nat_Onat @ ( C @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(722,axiom,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ c_Nat__Transfer_Ois__nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
thf(7518,plain,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ c_Nat__Transfer_Ois__nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(2780,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Relation_OImage ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__def) ).
thf(15627,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Relation_OImage ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2780]) ).
thf(3397,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__def) ).
thf(18063,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3397]) ).
thf(2006,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(12489,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2006]) ).
thf(3744,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) )
= A )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
thf(19507,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) )
= A )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3744]) ).
thf(2065,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__top )
=> ( ( A @ ( B @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__top__left) ).
thf(12705,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__top )
=> ( ( A @ ( B @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2065]) ).
thf(1466,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).
thf(10374,plain,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(1169,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__all) ).
thf(9164,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(1606,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_List_Oupto__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_List_Oupto__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto_Opinduct) ).
thf(10947,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_List_Oupto__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_List_Oupto__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1606]) ).
thf(2678,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ ( C @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__ImageI) ).
thf(15258,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ ( C @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2678]) ).
thf(3150,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
<=> ! [C: $i] : ( A @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
thf(17110,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( A @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) )
& ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ! [C: $i] : ( A @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3150]) ).
thf(54,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
thf(4910,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1091,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Opred ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min__right) ).
thf(8842,plain,
! [A: $i] :
( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Opred ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(1909,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
thf(12132,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1909]) ).
thf(2032,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__insert) ).
thf(12565,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2032]) ).
thf(3948,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBB ) ) @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib2) ).
thf(20294,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBB ) ) @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3948]) ).
thf(3568,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_Othe__elem ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_fequal @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OThe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__def) ).
thf(18796,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_Othe__elem ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_fequal @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OThe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3568]) ).
thf(1293,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_List_OtakeWhile ) ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Ofst ) @ ( C @ ( D @ ( E @ tc_prod ) @ ( tc_HOL_Obool @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_OtakeWhile ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__takeWhile__fst) ).
thf(9688,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_List_OtakeWhile ) ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Ofst ) @ ( C @ ( D @ ( E @ tc_prod ) @ ( tc_HOL_Obool @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_OtakeWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(3958,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__eq) ).
thf(20326,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3958]) ).
thf(1493,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__distinct) ).
thf(10477,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493]) ).
thf(2369,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_OId__on ) @ ( C @ ( C @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id__on) ).
thf(13914,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_OId__on ) @ ( C @ ( C @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2369]) ).
thf(1139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Product__Type_Ofst ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_Ofst ) @ hAPP ) ) )
=> ( ( ( B @ ( C @ ( D @ c_Product__Type_Osnd ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_Osnd ) @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__eqI) ).
thf(9041,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Product__Type_Ofst ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_Ofst ) @ hAPP ) ) )
=> ( ( ( B @ ( C @ ( D @ c_Product__Type_Osnd ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_Osnd ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(2536,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(14693,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2536]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i,F: $i] :
( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
thf(6442,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i,F: $i] :
( ( ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1956,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__many) ).
thf(12300,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1956]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( A @ c_Int_Oring__1__class_OInts @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__0) ).
thf(4999,plain,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( A @ c_Int_Oring__1__class_OInts @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(3439,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ ( B @ c_Product__Type_OPair ) @ ( C @ ( B @ tc_prod ) @ ( C @ ( B @ c_COMBC ) ) @ hAPP ) @ ( C @ ( B @ tc_prod ) @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( B @ tc_prod ) @ ( B @ ( C @ tc_prod ) @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__inj__on) ).
thf(18261,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ ( B @ c_Product__Type_OPair ) @ ( C @ ( B @ tc_prod ) @ ( C @ ( B @ c_COMBC ) ) @ hAPP ) @ ( C @ ( B @ tc_prod ) @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( B @ tc_prod ) @ ( B @ ( C @ tc_prod ) @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3439]) ).
thf(4619,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).
thf(22874,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4619]) ).
thf(1797,axiom,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
=> ( ( B
= ( C @ ( A @ c_Hilbert__Choice_OEps ) ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exE__some) ).
thf(11704,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
=> ( ( B
= ( C @ ( A @ c_Hilbert__Choice_OEps ) ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1797]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) )
=> ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( F @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__nthD2) ).
thf(4925,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) )
=> ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( F @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1584,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).
thf(10855,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584]) ).
thf(1725,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I4_J) ).
thf(11424,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725]) ).
thf(1056,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__map) ).
thf(8712,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(1899,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oord )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__iff) ).
thf(12100,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oord )
=> ( ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1899]) ).
thf(2614,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( D @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
!= ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I3_J) ).
thf(15014,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( D @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
!= ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2614]) ).
thf(1795,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__neg) ).
thf(11698,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1795]) ).
thf(1973,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( A @ ( B @ c_Relation_Orefl__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
thf(12365,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( A @ ( B @ c_Relation_Orefl__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1973]) ).
thf(1754,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).
thf(11545,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754]) ).
thf(1262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div) ).
thf(9544,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(2841,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [H: $i] :
( ( A @ ( B @ ( H @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__iff) ).
thf(15873,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( A @ ( B @ ( H @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [H: $i] :
( ( A @ ( B @ ( H @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2841]) ).
thf(947,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(8329,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1000,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ c_List_Osublist ) ) )
= ( B @ ( A @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__upt__eq__take) ).
thf(8513,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ c_List_Osublist ) ) )
= ( B @ ( A @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(3252,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
thf(17509,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3252]) ).
thf(3894,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( E @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__subset__eq) ).
thf(20108,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( E @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( E @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3894]) ).
thf(91,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(5049,plain,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1902,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__diff) ).
thf(12110,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1902]) ).
thf(4299,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Oinsert ) ) )
= ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Nil) ).
thf(21691,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Oinsert ) ) )
= ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4299]) ).
thf(2935,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq) ).
thf(16259,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2935]) ).
thf(2208,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I3_J) ).
thf(13260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2208]) ).
thf(951,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).
thf(8343,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(4417,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weaken) ).
thf(22136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4417]) ).
thf(4688,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff1__fold__graph) ).
thf(23126,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4688]) ).
thf(3162,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(17178,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3162]) ).
thf(3014,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__lower) ).
thf(16592,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3014]) ).
thf(3136,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( B @ c_member @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_HOL_OAll @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__eq) ).
thf(17061,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( B @ c_member @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_HOL_OAll @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3136]) ).
thf(3985,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__E) ).
thf(20416,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3985]) ).
thf(4617,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).
thf(22867,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4617]) ).
thf(1745,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Olast ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__snoc) ).
thf(11520,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Olast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745]) ).
thf(4229,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__UNIV) ).
thf(21402,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4229]) ).
thf(4427,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= A )
=> ( ( B @ ( E @ c_Set_OPow @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( D @ c_Set_OPow @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__surj) ).
thf(22169,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= A )
=> ( ( B @ ( E @ c_Set_OPow @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( D @ c_Set_OPow @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4427]) ).
thf(1702,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).
thf(11339,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( A @ ( B @ ( D @ ( C @ c_List_Olinorder__class_Osort__key ) ) ) @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__sort__key) ).
thf(5611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( A @ ( B @ ( D @ ( C @ c_List_Olinorder__class_Osort__key ) ) ) @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(3847,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__delta) ).
thf(19935,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3847]) ).
thf(4064,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist__ex1 ) ) )
<=> ? [D: $i] :
( ! [E: $i] :
( ( ( E @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E = D ) )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex1__iff) ).
thf(20684,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ! [E: $i] :
( ( ( E @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E = D ) )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Olist__ex1 ) ) ) )
& ( ( A @ ( B @ ( C @ c_List_Olist__ex1 ) ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( ( E @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E = D ) )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4064]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).
thf(6079,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(928,axiom,
tc_Int_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
thf(8265,plain,
tc_Int_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(1071,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsL) ).
thf(8778,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(3083,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( D @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) )
= A )
=> ( A @ ( B @ ( E @ ( F @ ( G @ c_Fun_Obij__betw ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__subset) ).
thf(16861,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( D @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) )
= A )
=> ( A @ ( B @ ( E @ ( F @ ( G @ c_Fun_Obij__betw ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3083]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).
thf(6122,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1946,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(12260,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1946]) ).
thf(556,axiom,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= A )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
thf(6897,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= A )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1804,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__take) ).
thf(11730,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1804]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__of__nat) ).
thf(5670,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(771,axiom,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__reflcl) ).
thf(7703,plain,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(1425,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__divide) ).
thf(10171,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(1346,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__eq__fold__idem) ).
thf(9861,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(412,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).
thf(6247,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(4565,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I3_J) ).
thf(22667,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4565]) ).
thf(2370,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__set__diff) ).
thf(13917,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2370]) ).
thf(1715,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit0) ).
thf(11388,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715]) ).
thf(2350,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) )
= ( B @ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__filter) ).
thf(13850,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) )
= ( B @ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2350]) ).
thf(3156,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ class_Enum_Oenum )
& ( C @ class_Enum_Oenum ) )
=> ( ( A @ ( C @ ( B @ tc_prod ) @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL )
<=> ( C @ ( B @ c_Product__Type_OPair ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( C @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( B @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__all @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_enum__all__prod__def) ).
thf(17146,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ class_Enum_Oenum )
& ( C @ class_Enum_Oenum ) )
=> ( ( ( C @ ( B @ c_Product__Type_OPair ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( C @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( B @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__all @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ tc_prod ) @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( B @ tc_prod ) @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL )
=> ( C @ ( B @ c_Product__Type_OPair ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( C @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( B @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__all @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3156]) ).
thf(2830,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_relpow_Osimps_I2_J) ).
thf(15843,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2830]) ).
thf(23816,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4741,4729]) ).
thf(23885,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= B )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23816]) ).
thf(23913,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23885]) ).
thf(2458,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Wellfounded_Oacc ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downward) ).
thf(14357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Wellfounded_Oacc ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2458]) ).
thf(1771,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( G @ ( H @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( H @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( G @ ( H @ c_Product__Type_OPair ) @ ( C @ ( G @ ( H @ tc_prod ) @ ( G @ c_COMBB ) ) @ ( H @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ ( H @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( F @ ( G @ ( H @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( H @ ( F @ ( C @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( C @ ( H @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__zip__map2) ).
thf(11619,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( G @ ( H @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( H @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( G @ ( H @ c_Product__Type_OPair ) @ ( C @ ( G @ ( H @ tc_prod ) @ ( G @ c_COMBB ) ) @ ( H @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ ( H @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( F @ ( G @ ( H @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( H @ ( F @ ( C @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( C @ ( H @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771]) ).
thf(3460,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(18325,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3460]) ).
thf(2982,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
thf(16460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2982]) ).
thf(2015,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( E @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(12510,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( E @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2015]) ).
thf(1540,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
thf(10699,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(2897,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) )
=> ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__decr) ).
thf(16104,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) )
=> ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2897]) ).
thf(3528,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__mono) ).
thf(18600,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3528]) ).
thf(4556,axiom,
tc_HOL_Obool @ class_Orderings_Otop,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
thf(22635,plain,
tc_HOL_Obool @ class_Orderings_Otop,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4556]) ).
thf(1630,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oconcat ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Oappend @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__conv__foldl) ).
thf(11037,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oconcat ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Oappend @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630]) ).
thf(1617,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( B
!= ( C @ c_Groups_Oone__class_Oone ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_geometric__sum) ).
thf(10990,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( B
!= ( C @ c_Groups_Oone__class_Oone ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617]) ).
thf(2663,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( H @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( E @ ( G @ ( H @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( G @ ( H @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( C @ ( G @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( G @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( H @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( E @ ( C @ ( H @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( C @ ( G @ ( H @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( H @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__subset__Sigma) ).
thf(15206,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( H @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( E @ ( G @ ( H @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( G @ ( H @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( C @ ( G @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( G @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( H @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( E @ ( C @ ( H @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( C @ ( G @ ( H @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( H @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2663]) ).
thf(3794,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mono__iff) ).
thf(19703,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3794]) ).
thf(4463,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
thf(22293,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4463]) ).
thf(44,axiom,
( ( c_Int_OMin @ c_Int_Osucc )
= c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Min) ).
thf(4878,plain,
( ( c_Int_OMin @ c_Int_Osucc )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(5510,plain,
~ ? [A: $i] :
( ( A @ c_Code__Numeral_OSuc__code__numeral )
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) ),
inference(miniscope,[status(thm)],[5509]) ).
thf(5511,plain,
! [A: $i] :
( ( A @ c_Code__Numeral_OSuc__code__numeral )
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) ),
inference(cnf,[status(esa)],[5510]) ).
thf(5512,plain,
! [A: $i] :
( ( A @ c_Code__Numeral_OSuc__code__numeral )
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[5511]) ).
thf(4535,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistset ) )
= ( A @ ( C @ c_List_Olistset ) @ ( B @ ( C @ c_List_Oset__Cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listset_Osimps_I2_J) ).
thf(22559,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistset ) )
= ( A @ ( C @ c_List_Olistset ) @ ( B @ ( C @ c_List_Oset__Cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4535]) ).
thf(3805,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
thf(19744,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3805]) ).
thf(4250,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Odistrib__lattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib1) ).
thf(21502,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Odistrib__lattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4250]) ).
thf(2282,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) )
<=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ball__set__replicate) ).
thf(13572,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) )
=> ! [E: $i] :
( ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [E: $i] :
( ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) )
=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2282]) ).
thf(1585,axiom,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__code__numeral__def) ).
thf(10858,plain,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585]) ).
thf(2965,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( D @ c_List_Olist_Olist__size ) ) @ ( C @ ( B @ ( D @ c_List_Olist_Olist__size ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__pointwise) ).
thf(16386,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( D @ c_List_Olist_Olist__size ) ) @ ( C @ ( B @ ( D @ c_List_Olist_Olist__size ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2965]) ).
thf(4000,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__distrib2) ).
thf(20459,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4000]) ).
thf(2924,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).
thf(16215,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2924]) ).
thf(1926,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OAll @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__def) ).
thf(12190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OAll @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1926]) ).
thf(4608,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_Oconversep ) ) )
= ( A @ ( C @ ( D @ c_Predicate_Oconversep ) ) @ ( B @ ( C @ ( D @ c_Predicate_Oconversep ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__meet) ).
thf(22832,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_Oconversep ) ) )
= ( A @ ( C @ ( D @ c_Predicate_Oconversep ) ) @ ( B @ ( C @ ( D @ c_Predicate_Oconversep ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4608]) ).
thf(2298,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ hAPP ) )
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__diff1) ).
thf(13649,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ hAPP ) )
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2298]) ).
thf(3907,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset) ).
thf(20152,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3907]) ).
thf(4267,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( A
= ( B @ ( c_Int_OAbs__Integ @ hAPP ) ) )
=> ~ ( c_Int_OInteg @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__cases) ).
thf(21564,plain,
! [A: $i] :
~ ! [B: $i] :
( ( A
= ( B @ ( c_Int_OAbs__Integ @ hAPP ) ) )
=> ~ ( c_Int_OInteg @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4267]) ).
thf(3295,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
thf(17670,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3295]) ).
thf(1580,axiom,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
thf(10843,plain,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580]) ).
thf(1673,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) )
= A )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__eqD) ).
thf(11217,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) )
= A )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673]) ).
thf(3683,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__upto) ).
thf(19231,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3683]) ).
thf(277,axiom,
! [A: $i] :
~ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__int) ).
thf(5719,plain,
! [A: $i] :
~ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(1482,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
thf(10426,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(4403,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__Suc) ).
thf(22092,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4403]) ).
thf(2256,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI) ).
thf(13472,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2256]) ).
thf(3053,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold) ).
thf(16751,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3053]) ).
thf(2752,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__ub__add__nat) ).
thf(15531,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2752]) ).
thf(3415,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(18151,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3415]) ).
thf(1526,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__times__mod__eq) ).
thf(10612,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526]) ).
thf(4495,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( c_fFalse @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ c_COMBK ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_falseE) ).
thf(22400,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( c_fFalse @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ c_COMBK ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4495]) ).
thf(2516,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD2) ).
thf(14605,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2516]) ).
thf(1062,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(8724,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(1776,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( A @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ ( A @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_List_Obutlast ) @ ( A @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).
thf(11634,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( A @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ ( A @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_List_Obutlast ) @ ( A @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776]) ).
thf(1342,axiom,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ c_Nat__Transfer_Ois__nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).
thf(9849,plain,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ c_Nat__Transfer_Ois__nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(7084,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(2499,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image) ).
thf(14524,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2499]) ).
thf(211,axiom,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(5470,plain,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(2112,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
thf(12846,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2112]) ).
thf(3084,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ c_Nat_Ocompow ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).
thf(16865,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ c_Nat_Ocompow ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3084]) ).
thf(2721,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1) ).
thf(15407,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2721]) ).
thf(3589,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_ODomain ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Relation_ODomain ) @ hAPP ) @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__insert) ).
thf(18873,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_ODomain ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Relation_ODomain ) @ hAPP ) @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3589]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( D @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( B @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( ( B @ ( C @ c_List_Oconcat ) )
= ( A @ ( C @ c_List_Oconcat ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__eq__concat__iff) ).
thf(7428,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( D @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( B @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_List_Oconcat ) )
= ( A @ ( C @ c_List_Oconcat ) ) ) )
& ( ( ( B @ ( C @ c_List_Oconcat ) )
= ( A @ ( C @ c_List_Oconcat ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__less__iff) ).
thf(4785,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4429,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__DSequence_Opos__map ) ) ) ) )
= ( A @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ c_Lazy__Sequence_Omap ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__map__def) ).
thf(22176,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__DSequence_Opos__map ) ) ) ) )
= ( A @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ c_Lazy__Sequence_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4429]) ).
thf(23766,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4735,23748]) ).
thf(23777,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= B )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23766]) ).
thf(23784,plain,
! [A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Oone__class_Oone @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[23777]) ).
thf(2192,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( E @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
thf(13218,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( E @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2192]) ).
thf(3165,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
thf(17193,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3165]) ).
thf(3827,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__nonneg__0) ).
thf(19818,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3827]) ).
thf(3016,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_OF__eq) ).
thf(16597,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3016]) ).
thf(2161,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__subsets) ).
thf(13078,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2161]) ).
thf(1756,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(11565,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756]) ).
thf(4399,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
thf(22082,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4399]) ).
thf(1931,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__assoc) ).
thf(12215,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1931]) ).
thf(3501,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
thf(18503,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3501]) ).
thf(3353,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
thf(17876,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3353]) ).
thf(392,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod2__Suc__Suc) ).
thf(6178,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(4480,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I2_J) ).
thf(22346,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4480]) ).
thf(2243,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil )
!= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
thf(13401,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil )
!= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2243]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).
thf(6509,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ tc_prod ) @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Nil) ).
thf(7906,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ tc_prod ) @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(4694,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
thf(23148,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4694]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
thf(6232,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(25761,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,23914]) ).
thf(25762,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[25761]) ).
thf(25763,plain,
( ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[25762:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(39030,plain,
( ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(rewrite,[status(thm)],[25763,7678]) ).
thf(7145,plain,
~ ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(polarity_switch,[status(thm)],[7144]) ).
thf(26613,plain,
( ( ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8089,7145]) ).
thf(26614,plain,
( ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[26613]) ).
thf(26626,plain,
( ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) )
!= c_fTrue ),
inference(simp,[status(thm)],[26614]) ).
thf(1666,axiom,
! [A: $i] :
( ( A @ c_Nitpick_Oone__frac )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ c_Nitpick_OAbs__Frac ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oone__frac__def) ).
thf(11191,plain,
! [A: $i] :
( ( A @ c_Nitpick_Oone__frac )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ c_Nitpick_OAbs__Frac ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666]) ).
thf(3575,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ ( F @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex) ).
thf(18821,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ ( F @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3575]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__abs__iff) ).
thf(7244,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(1640,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
thf(11074,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640]) ).
thf(2729,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( H @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( E @ ( D @ ( H @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( C @ ( G @ tc_prod ) @ ( D @ ( H @ tc_prod ) @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__inj__on) ).
thf(15439,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( H @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( E @ ( D @ ( H @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( C @ ( G @ tc_prod ) @ ( D @ ( H @ tc_prod ) @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2729]) ).
thf(2389,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
thf(14000,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2389]) ).
thf(2203,axiom,
c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).
thf(13250,plain,
c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2203]) ).
thf(3360,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__eq) ).
thf(17902,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3360]) ).
thf(995,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__assoc) ).
thf(8491,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(4148,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
thf(21083,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4148]) ).
thf(1036,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_List_Oupt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__upt) ).
thf(8623,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_List_Oupt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(2770,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(15595,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2770]) ).
thf(1172,axiom,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__mod) ).
thf(9177,plain,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(1254,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oreplicate ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__replicate) ).
thf(9512,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oreplicate ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(3753,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(19539,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3753]) ).
thf(2957,axiom,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( B @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ ( B @ ( B @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fold__inf) ).
thf(16360,plain,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( B @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ ( B @ ( B @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2957]) ).
thf(613,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oremdups ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remdups__card__conv) ).
thf(7097,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oremdups ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(2533,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).
thf(14680,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2533]) ).
thf(291,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(5769,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1544,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append__length) ).
thf(10721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544]) ).
thf(4281,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__mono) ).
thf(21628,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4281]) ).
thf(2328,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__leq @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omin__weak @ ( A @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omin__weak @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmin__insertI) ).
thf(13778,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__leq @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omin__weak @ ( A @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omin__weak @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2328]) ).
thf(3321,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
thf(17755,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3321]) ).
thf(3480,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
thf(18415,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3480]) ).
thf(1222,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).
thf(9380,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(3183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( A @ ( D @ ( F @ ( E @ c_Relation_OImage ) ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__INT__subset) ).
thf(17245,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( A @ ( D @ ( F @ ( E @ c_Relation_OImage ) ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3183]) ).
thf(2278,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Predicate_OPowp ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ c_Set_OPow @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__Pow__eq) ).
thf(13551,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Set_OPow @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Predicate_OPowp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Predicate_OPowp ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Set_OPow @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2278]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__assoc) ).
thf(6926,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(3607,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I4_J) ).
thf(18937,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3607]) ).
thf(2086,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(12764,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2086]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__same__eq) ).
thf(5702,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(3068,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( E @ ( B @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__key__triv) ).
thf(16801,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( E @ ( B @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3068]) ).
thf(3689,axiom,
! [A: $i] :
( ( A @ c_Fun_Oid @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) )
= ( A @ c_Fun_Oid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__id) ).
thf(19273,plain,
! [A: $i] :
( ( A @ c_Fun_Oid @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) )
= ( A @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3689]) ).
thf(1266,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).
thf(9554,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(2469,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(14401,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2469]) ).
thf(3404,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__replicate) ).
thf(18087,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3404]) ).
thf(4371,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Otop )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
= ( C @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
thf(21979,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Otop )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
= ( C @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4371]) ).
thf(1530,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
<=> ( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Ofst ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( C
= ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Ofst ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__def) ).
thf(10634,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Ofst ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( C
= ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Ofst ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
=> ( A @ ( B @ ( C @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Ofst ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( C
= ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Ofst ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530]) ).
thf(1104,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__beyond) ).
thf(8920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(1392,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__drop_H) ).
thf(10038,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( ( B @ ( D @ ( C @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= A )
<=> ( ( ( A @ ( C @ ( E @ c_Product__Type_Osnd ) @ ( C @ ( C @ ( E @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= B )
& ( ( A @ ( C @ ( E @ c_Product__Type_Ofst ) @ ( E @ ( C @ ( E @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__eq__conv) ).
thf(5983,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( ( ( ( A @ ( C @ ( E @ c_Product__Type_Osnd ) @ ( C @ ( C @ ( E @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= B )
& ( ( A @ ( C @ ( E @ c_Product__Type_Ofst ) @ ( E @ ( C @ ( E @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= D ) )
=> ( ( B @ ( D @ ( C @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= A ) )
& ( ( ( B @ ( D @ ( C @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= A )
=> ( ( ( A @ ( C @ ( E @ c_Product__Type_Osnd ) @ ( C @ ( C @ ( E @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= B )
& ( ( A @ ( C @ ( E @ c_Product__Type_Ofst ) @ ( E @ ( C @ ( E @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1498,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Onth @ hAPP ) @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth_Osimps) ).
thf(10502,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Onth @ hAPP ) @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(2428,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(14217,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2428]) ).
thf(2961,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__f__f) ).
thf(16371,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2961]) ).
thf(3812,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(19768,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3812]) ).
thf(2814,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_ORange ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Un__eq) ).
thf(15756,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_ORange ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2814]) ).
thf(961,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__drop) ).
thf(8371,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(813,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(7842,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(4651,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) @ hBOOL )
=> ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__induct) ).
thf(23005,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) @ hBOOL )
=> ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4651]) ).
thf(1074,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of1) ).
thf(8788,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(3463,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
thf(18340,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3463]) ).
thf(1912,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).
thf(12147,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1912]) ).
thf(1963,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__0) ).
thf(12340,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1963]) ).
thf(2296,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ ( F @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( C
= ( D @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( ! [I: $i] :
( ( D @ ( I @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( B @ hAPP ) )
= ( I @ ( E @ ( A @ ( G @ ( H @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) ) ) )
=> ( ( C @ ( A @ ( H @ ( F @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( H @ ( G @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strong__setprod__reindex__cong) ).
thf(13639,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ ( F @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( C
= ( D @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( ! [I: $i] :
( ( D @ ( I @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( B @ hAPP ) )
= ( I @ ( E @ ( A @ ( G @ ( H @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) ) ) )
=> ( ( C @ ( A @ ( H @ ( F @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( H @ ( G @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2296]) ).
thf(636,axiom,
! [A: $i] : ( A @ c_List_Olist_ONil @ ( A @ c_List_Odistinct @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
thf(7185,plain,
! [A: $i] : ( A @ c_List_Olist_ONil @ ( A @ c_List_Odistinct @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(1568,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
thf(10808,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568]) ).
thf(4286,axiom,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exists__code) ).
thf(21641,plain,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) )
& ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4286]) ).
thf(1489,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_COMBI @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__odd__number__of) ).
thf(10462,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_COMBI @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(3635,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ hAPP ) )
= D )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( F @ ( C @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( E @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageI) ).
thf(19058,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ hAPP ) )
= D )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( F @ ( C @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( E @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3635]) ).
thf(1960,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I2_J) ).
thf(12321,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1960]) ).
thf(888,axiom,
tc_Int_Oint @ class_Groups_Ogroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
thf(8145,plain,
tc_Int_Oint @ class_Groups_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(4380,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Int) ).
thf(22015,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4380]) ).
thf(2487,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
thf(14477,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2487]) ).
thf(4407,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).
thf(22104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4407]) ).
thf(788,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) )
= ( A @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__eq__drop) ).
thf(7762,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) )
= ( A @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(3351,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_Otrans ) )
=> ( ( A @ ( C @ c_Relation_Otrans ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Otrans ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Int) ).
thf(17870,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_Otrans ) )
=> ( ( A @ ( C @ c_Relation_Otrans ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Otrans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3351]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(6043,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(2713,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_FunDef_Orp__inv__image ) )
= ( A @ ( B @ c_Relation_Oinv__image ) @ ( A @ ( B @ c_Relation_Oinv__image ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ ( B @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ c_COMBS ) ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__def) ).
thf(15383,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_FunDef_Orp__inv__image ) )
= ( A @ ( B @ c_Relation_Oinv__image ) @ ( A @ ( B @ c_Relation_Oinv__image ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ ( B @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ c_COMBS ) ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2713]) ).
thf(2290,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ c_List_Osublist ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__set__sublistI) ).
thf(13612,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ c_List_Osublist ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2290]) ).
thf(3990,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__Int) ).
thf(20427,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3990]) ).
thf(1328,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
!= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq__if__length__neq) ).
thf(9790,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
!= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(2872,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD2) ).
thf(15994,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2872]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__mult) ).
thf(4755,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4756,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_Rings_Oring__1 ) ),
inference(cnf,[status(esa)],[4755]) ).
thf(4757,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ class_Rings_Oring__1 )
| ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4756]) ).
thf(4512,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_asm) ).
thf(22471,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4512]) ).
thf(3447,axiom,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(18283,plain,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3447]) ).
thf(3677,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(19214,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3677]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
<=> ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__converse) ).
thf(5690,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( A @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_Orefl__on ) ) ) )
& ( ( A @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(2274,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__Un) ).
thf(13536,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2274]) ).
thf(1198,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( B
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).
thf(9277,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( B
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(4469,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).
thf(22310,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4469]) ).
thf(1464,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(10369,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(4324,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq) ).
thf(21809,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4324]) ).
thf(3996,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( A @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD2) ).
thf(20444,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( A @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3996]) ).
thf(3221,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetI) ).
thf(17385,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3221]) ).
thf(4150,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).
thf(21095,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4150]) ).
thf(3095,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).
thf(16916,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3095]) ).
thf(13789,plain,
! [A: $i] : ( A @ tc_List_Olist @ class_Nat_Osize ),
inference(cnf,[status(esa)],[13788]) ).
thf(2160,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Groups_Ocomm__monoid__mult )
& ( E @ class_Groups_Ocomm__monoid__add ) )
=> ( ( D = C )
=> ( ( C @ c_Nat__Transfer_Onat__set )
=> ( ! [F: $i] :
( ( F @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) )
=> ( ( D @ ( B @ ( E @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I1_J) ).
thf(13070,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Groups_Ocomm__monoid__mult )
& ( E @ class_Groups_Ocomm__monoid__add ) )
=> ( ( D = C )
=> ( ( C @ c_Nat__Transfer_Onat__set )
=> ( ! [F: $i] :
( ( F @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) )
=> ( ( D @ ( B @ ( E @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2160]) ).
thf(1682,axiom,
tc_Int_Oint @ class_Rings_Oring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(11249,plain,
tc_Int_Oint @ class_Rings_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682]) ).
thf(2062,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I17_J) ).
thf(12692,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2062]) ).
thf(4339,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__UN) ).
thf(21855,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4339]) ).
thf(4077,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oset @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Set_OCollect @ hAPP ) @ ( C @ tc_List_Olist @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lists__length__eq) ).
thf(20758,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oset @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Set_OCollect @ hAPP ) @ ( C @ tc_List_Olist @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4077]) ).
thf(2880,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__insert) ).
thf(16026,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2880]) ).
thf(2273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq) ).
thf(13530,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2273]) ).
thf(1224,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oremove1 ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__insort) ).
thf(9391,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oremove1 ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(2741,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
thf(15491,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2741]) ).
thf(4180,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
thf(21219,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4180]) ).
thf(1202,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olenlex ) )
= ( B @ tc_List_Olist @ c_COMBI @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ tc_prod ) @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ tc_prod ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Olex ) @ ( c_Wellfounded_Oless__than @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lenlex__def) ).
thf(9301,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olenlex ) )
= ( B @ tc_List_Olist @ c_COMBI @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ tc_prod ) @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ tc_prod ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Olex ) @ ( c_Wellfounded_Oless__than @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(45118,plain,
! [B: $i,A: $i] :
( ( ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
!= ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( c_Int_OPls @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(paramod_ordered,[status(thm)],[8226,4729]) ).
thf(45443,plain,
! [B: $i,A: $i] :
( ( c_Int_OPls != A )
| ( ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( c_Int_OPls @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[45118]) ).
thf(45784,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( c_Int_OPls @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[45443]) ).
thf(543,axiom,
c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ c_Wellfounded_Owf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__less__than) ).
thf(6833,plain,
c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ c_Wellfounded_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C
= ( B @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).
thf(7501,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C
= ( B @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(2267,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(13513,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2267]) ).
thf(13514,plain,
~ ? [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(miniscope,[status(thm)],[13513]) ).
thf(13515,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(cnf,[status(esa)],[13514]) ).
thf(13516,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[13515]) ).
thf(32918,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( c_Nat_OSuc @ hAPP ) ) )
| ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4741,13516]) ).
thf(32927,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= B )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= c_Nat_OSuc )
| ( A != tc_Nat_Onat )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[32918]) ).
thf(32964,plain,
( ( ( tc_Nat_Onat @ c_Int_Oring__1__class_Oof__int )
!= c_Nat_OSuc )
| ~ ( tc_Nat_Onat @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[32927]) ).
thf(32965,plain,
( ( ( tc_Nat_Onat @ class_Rings_Oring__1 )
!= ( tc_Int_Oint @ class_Rings_Oring__1 ) )
| ( ( tc_Nat_Onat @ c_Int_Oring__1__class_Oof__int )
!= c_Nat_OSuc )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,32964]) ).
thf(32966,plain,
( ( ( tc_Nat_Onat @ class_Rings_Oring__1 )
!= ( tc_Int_Oint @ class_Rings_Oring__1 ) )
| ( ( tc_Nat_Onat @ c_Int_Oring__1__class_Oof__int )
!= c_Nat_OSuc ) ),
inference(simp,[status(thm)],[32965]) ).
thf(32967,plain,
( ( tc_Nat_Onat != tc_Int_Oint )
| ( ( tc_Nat_Onat @ c_Int_Oring__1__class_Oof__int )
!= c_Nat_OSuc ) ),
inference(simp,[status(thm)],[32966]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
<=> ( ! [F: $i] :
( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( F @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( F @ ( B @ ( E @ c_List_Onth @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__conv__all__nth) ).
thf(5113,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ! [F: $i] :
( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( F @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( F @ ( B @ ( E @ c_List_Onth @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
=> ( ! [F: $i] :
( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( F @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( F @ ( B @ ( E @ c_List_Onth @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1780,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(11646,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780]) ).
thf(9732,plain,
~ ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
inference(polarity_switch,[status(thm)],[9731]) ).
thf(26619,plain,
( ( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8089,9732]) ).
thf(26620,plain,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[26619]) ).
thf(26627,plain,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) )
!= c_fTrue ),
inference(simp,[status(thm)],[26620]) ).
thf(33131,plain,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) )
!= c_fTrue ),
inference(rewrite,[status(thm)],[26627,4775]) ).
thf(3569,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I9_J) ).
thf(18799,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3569]) ).
thf(1118,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(8964,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(2709,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__0) ).
thf(15368,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2709]) ).
thf(1093,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
<=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( B = A ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).
thf(8847,plain,
! [A: $i,B: $i] :
( ( ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( B = A ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( B = A ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(2150,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(13023,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2150]) ).
thf(2128,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oall__interval__int ) ) )
<=> ! [D: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( D @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__interval__int__def) ).
thf(12930,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( D @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Oall__interval__int ) ) ) )
& ( ( A @ ( B @ ( C @ c_List_Oall__interval__int ) ) )
=> ! [D: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( D @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2128]) ).
thf(3458,axiom,
! [A: $i] :
( ( A @ c_Nat__Transfer_Onat__set )
<=> ! [B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__set__def) ).
thf(18315,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ c_Nat__Transfer_Onat__set ) )
& ( ( A @ c_Nat__Transfer_Onat__set )
=> ! [B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3458]) ).
thf(1609,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I11_J) ).
thf(10958,plain,
! [A: $i] :
( ( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609]) ).
thf(4641,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
thf(22967,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4641]) ).
thf(438,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__0__number__of) ).
thf(6402,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(2756,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supE) ).
thf(15546,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2756]) ).
thf(3030,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__disjoint) ).
thf(16652,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3030]) ).
thf(4492,axiom,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
thf(22393,plain,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4492]) ).
thf(4074,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( G @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( D @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( E @ ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( G @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ ( G @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( F @ ( D @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__comp) ).
thf(20745,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( G @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( D @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( E @ ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( G @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ ( G @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( F @ ( D @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4074]) ).
thf(2686,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__le) ).
thf(15279,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2686]) ).
thf(3494,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( F @ ( G @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ! [H: $i,I: $i] :
( ( A @ ( I @ ( H @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( F @ ( G @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( I @ ( H @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
thf(18481,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( F @ ( G @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ! [H: $i,I: $i] :
( ( A @ ( I @ ( H @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( F @ ( G @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( I @ ( H @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3494]) ).
thf(2790,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__eq) ).
thf(15670,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2790]) ).
thf(2392,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(14013,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2392]) ).
thf(1527,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( c_Int_Onat @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__nat__eq__if) ).
thf(10615,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( c_Int_Onat @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(500,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Nat_Osize,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osize) ).
thf(6666,plain,
tc_Code__Numeral_Ocode__numeral @ class_Nat_Osize,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1354,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of) ).
thf(9885,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(4655,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I5_J) ).
thf(23018,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4655]) ).
thf(3724,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( F @ c_Fun_Oid @ ( E @ ( F @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ( ( A @ ( C @ hAPP ) @ ( D @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__id__dest) ).
thf(19405,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( F @ c_Fun_Oid @ ( E @ ( F @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ( ( A @ ( C @ hAPP ) @ ( D @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3724]) ).
thf(2245,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__int__conv) ).
thf(13411,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2245]) ).
thf(2406,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).
thf(14100,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2406]) ).
thf(3308,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( H @ ( I @ ( J @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( E @ ( H @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ ( J @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
=> ( ( I @ ( B @ ( J @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( G @ ( G @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( J @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( J @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( J @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( H @ ( J @ ( J @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( J @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class2) ).
thf(17709,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( H @ ( I @ ( J @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( E @ ( H @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ ( J @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
=> ( ( I @ ( B @ ( J @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( G @ ( G @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( J @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( J @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( J @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( H @ ( J @ ( J @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( J @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3308]) ).
thf(3039,axiom,
( ( c_fFalse @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).
thf(16691,plain,
( ( c_fFalse @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3039]) ).
thf(16692,plain,
( ( c_fFalse @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[16691]) ).
thf(43845,plain,
( ( c_fFalse @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Orderings_Obot__class_Obot ) ),
inference(rewrite,[status(thm)],[16692,20483]) ).
thf(1349,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zdiv__mult__2) ).
thf(9868,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(1764,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(11602,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764]) ).
thf(2351,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( A @ ( D @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( D @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp) ).
thf(13853,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( A @ ( D @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( D @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2351]) ).
thf(1020,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__add) ).
thf(8577,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(3620,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OnegateSnd @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negateSnd__eq) ).
thf(18989,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OnegateSnd @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3620]) ).
thf(3142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ouminus )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__apply) ).
thf(17086,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ouminus )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3142]) ).
thf(3286,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image ) ) ) ) )
=> ( ( C @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [I: $i] :
( ( C @ ( I @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( B @ hAPP ) )
= ( I @ ( A @ hAPP ) ) ) )
=> ( ( C @ ( B @ ( D @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Ocong) ).
thf(17638,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image ) ) ) ) )
=> ( ( C @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [I: $i] :
( ( C @ ( I @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( B @ hAPP ) )
= ( I @ ( A @ hAPP ) ) ) )
=> ( ( C @ ( B @ ( D @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3286]) ).
thf(2209,axiom,
tc_Int_Oint @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Odistrib__lattice) ).
thf(13269,plain,
tc_Int_Oint @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2209]) ).
thf(177,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).
thf(5330,plain,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(3932,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Fun_Oid @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__id) ).
thf(20244,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Fun_Oid @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3932]) ).
thf(2467,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Equiv__Relations_Oquotient @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__quotient__disjoint) ).
thf(14395,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Equiv__Relations_Oquotient @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2467]) ).
thf(1281,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
thf(9641,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
thf(8518,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(2240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
~ ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainE) ).
thf(13391,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
~ ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2240]) ).
thf(2157,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( E @ ( F @ ( G @ ( H @ ( I @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( I @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( B @ ( C @ ( H @ ( D @ ( I @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( C @ ( D @ tc_prod ) @ ( H @ ( I @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( A @ hAPP ) @ ( G @ ( B @ hAPP ) @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__imageI) ).
thf(13063,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( E @ ( F @ ( G @ ( H @ ( I @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( I @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( B @ ( C @ ( H @ ( D @ ( I @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( C @ ( D @ tc_prod ) @ ( H @ ( I @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( A @ hAPP ) @ ( G @ ( B @ hAPP ) @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2157]) ).
thf(3822,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryD) ).
thf(19800,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3822]) ).
thf(1958,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( C @ ( G @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( B @ ( tc_HOL_Obool @ ( D @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Set_OCollect @ hAPP ) @ ( F @ c_Finite__Set_Ocard @ hAPP ) )
= ( G @ ( A @ hAPP ) ) ) )
=> ( ( E @ ( B @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ ( F @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__multicount__gen) ).
thf(12304,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( C @ ( G @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( B @ ( tc_HOL_Obool @ ( D @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Set_OCollect @ hAPP ) @ ( F @ c_Finite__Set_Ocard @ hAPP ) )
= ( G @ ( A @ hAPP ) ) ) )
=> ( ( E @ ( B @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ ( F @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1958]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int) ).
thf(5285,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(3801,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
thf(19731,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3801]) ).
thf(553,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).
thf(6888,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(4457,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ ( F @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I1) ).
thf(22269,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ ( F @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4457]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(6709,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(3954,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__eq__iff) ).
thf(20309,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3954]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).
thf(7923,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(4117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE2) ).
thf(20957,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4117]) ).
thf(1417,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(10131,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(514,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__imp__of__nat) ).
thf(6728,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(6215,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(4252,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oclosed) ).
thf(21511,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4252]) ).
thf(1677,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Osnd ) @ hAPP ) )
= ( A @ ( B @ c_COMBI @ ( C @ ( B @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__def) ).
thf(11234,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Osnd ) @ hAPP ) )
= ( A @ ( B @ c_COMBI @ ( C @ ( B @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__le__0__iff) ).
thf(4808,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(2077,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__wfD) ).
thf(12741,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2077]) ).
thf(2084,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( C @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__mono) ).
thf(12760,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( C @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2084]) ).
thf(531,axiom,
( ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Min) ).
thf(6795,plain,
( ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(785,axiom,
! [A: $i] :
( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Pls) ).
thf(7750,plain,
! [A: $i] :
( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(3880,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan__int) ).
thf(20052,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3880]) ).
thf(2049,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff2) ).
thf(12645,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2049]) ).
thf(1989,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(12422,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1989]) ).
thf(4158,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Range) ).
thf(21123,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4158]) ).
thf(2136,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onorm__frac__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onorm__frac__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Opinduct) ).
thf(12959,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onorm__frac__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onorm__frac__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2136]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__snd__zip) ).
thf(5854,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(680,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Osplice ) ) )
= ( A @ ( C @ ( E @ c_List_Osplice ) ) @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).
thf(7346,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Osplice ) ) )
= ( A @ ( C @ ( E @ c_List_Osplice ) ) @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(2868,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Orderings_Otop__class_Otop @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( C @ c_COMBC ) ) @ hAPP ) @ ( C @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__set__fold) ).
thf(15984,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Orderings_Otop__class_Otop @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( C @ c_COMBC ) ) @ hAPP ) @ ( C @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2868]) ).
thf(4710,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__self) ).
thf(23231,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4710]) ).
thf(3939,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(20264,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3939]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ c_List_Olast ) @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ c_List_OtakeWhile ) ) )
= ( B @ ( A @ c_List_Obutlast ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__not__last) ).
thf(6656,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ c_List_Olast ) @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ c_List_OtakeWhile ) ) )
= ( B @ ( A @ c_List_Obutlast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(1335,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Equiv__Relations_Oequivp ) )
<=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__def) ).
thf(9814,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) )
=> ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) )
=> ( A @ ( B @ c_Equiv__Relations_Oequivp ) ) )
& ( ( A @ ( B @ c_Equiv__Relations_Oequivp ) )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) )
=> ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(2463,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).
thf(14380,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2463]) ).
thf(3223,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).
thf(17395,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3223]) ).
thf(1968,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( A @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__O__subset) ).
thf(12353,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( A @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1968]) ).
thf(1052,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
thf(8694,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(3175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__sup__le) ).
thf(17225,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3175]) ).
thf(1006,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I2_J) ).
thf(8530,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(2695,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntI) ).
thf(15302,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2695]) ).
thf(2019,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ! [F: $i,G: $i] :
( ( G @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( G @ ( B @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ hAPP ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( E @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
thf(12521,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ! [F: $i,G: $i] :
( ( G @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( G @ ( B @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ hAPP ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( E @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2019]) ).
thf(4123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__subset__iff) ).
thf(20976,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4123]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(7281,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1246,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) )
=> ( ( B @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Otranspose ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ ( C @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__column) ).
thf(9493,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) )
=> ( ( B @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Otranspose ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ ( C @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(1708,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
thf(11356,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708]) ).
thf(1179,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ c_List_Oupt ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__map__upt) ).
thf(9196,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ c_List_Oupt ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(674,axiom,
! [A: $i] :
( ( ( A @ class_Orderings_Olinorder )
& ( A @ class_Lattices_Osemilattice__sup ) )
=> ( ( A @ c_Lattices_Osemilattice__sup__class_Osup )
= ( A @ c_Orderings_Oord__class_Omax ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__max) ).
thf(7329,plain,
! [A: $i] :
( ( ( A @ class_Orderings_Olinorder )
& ( A @ class_Lattices_Osemilattice__sup ) )
=> ( ( A @ c_Lattices_Osemilattice__sup__class_Osup )
= ( A @ c_Orderings_Oord__class_Omax ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(2825,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeast @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__0) ).
thf(15826,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeast @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2825]) ).
thf(2816,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i,E: $i] :
( ~ ( E @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A
= ( E @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__decomp__last) ).
thf(15761,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i,E: $i] :
( ~ ( E @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A
= ( E @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
=> ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i,E: $i] :
( ~ ( E @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A
= ( E @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2816]) ).
thf(3861,axiom,
( c_FunDef_Omin__weak
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_FunDef_Opair__leq @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__weak__def) ).
thf(19991,plain,
( c_FunDef_Omin__weak
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_FunDef_Opair__leq @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3861]) ).
thf(2171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ? [E: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
& ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__zero) ).
thf(13116,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ? [E: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
& ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2171]) ).
thf(4513,axiom,
! [A: $i] : ( A @ c_Wellfounded_Ofinite__psubset @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Wellfounded_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__finite__psubset) ).
thf(22473,plain,
! [A: $i] : ( A @ c_Wellfounded_Ofinite__psubset @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Wellfounded_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4513]) ).
thf(870,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
thf(8068,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(2674,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
thf(15243,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2674]) ).
thf(1652,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( ( ~ ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).
thf(11133,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( ( ~ ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( F @ ( G @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( H @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ ( D @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( H @ ( C @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( B @ ( H @ ( F @ ( G @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__update__cong) ).
thf(5609,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( F @ ( G @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( H @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ ( D @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( H @ ( C @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( B @ ( H @ ( F @ ( G @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ class_Groups_Omonoid__add )
=> ( ( A @ c_List_Olist_ONil @ ( A @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__simps_I1_J) ).
thf(5053,plain,
! [A: $i] :
( ( A @ class_Groups_Omonoid__add )
=> ( ( A @ c_List_Olist_ONil @ ( A @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(705,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= ( c_Int_Onat @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ ( tc_Int_Oint @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ ( B @ ( tc_Int_Oint @ ( D @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( c_Nat__Numeral_Oneg @ ( D @ c_If @ ( tc_Int_Oint @ ( D @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_fun ) @ ( D @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__number__of) ).
thf(7421,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= ( c_Int_Onat @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ ( tc_Int_Oint @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ ( B @ ( tc_Int_Oint @ ( D @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( c_Nat__Numeral_Oneg @ ( D @ c_If @ ( tc_Int_Oint @ ( D @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_fun ) @ ( D @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(3202,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( D @ ( B @ ( A @ ( F @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( C @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( F @ ( C @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( C @ ( E @ tc_prod ) @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Sigma) ).
thf(17306,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( D @ ( B @ ( A @ ( F @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( C @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( F @ ( C @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( C @ ( E @ tc_prod ) @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3202]) ).
thf(4676,axiom,
! [A: $i] : ( c_fFalse @ ( A @ ( tc_HOL_Obool @ c_COMBK ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ c_Wellfounded_OwfP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__empty) ).
thf(23091,plain,
! [A: $i] : ( c_fFalse @ ( A @ ( tc_HOL_Obool @ c_COMBK ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ c_Wellfounded_OwfP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4676]) ).
thf(3452,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV1) ).
thf(18293,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3452]) ).
thf(1161,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I3_J) ).
thf(9145,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(4293,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Ofoldr ) ) ) ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_List_Olist_ONil @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Ofoldr ) ) ) ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__max) ).
thf(21668,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Ofoldr ) ) ) ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_List_Olist_ONil @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Ofoldr ) ) ) ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4293]) ).
thf(2802,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(15714,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2802]) ).
thf(1594,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__drop) ).
thf(10887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594]) ).
thf(2216,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
thf(13297,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2216]) ).
thf(1331,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_New__DSequence_Opos__not__seq @ hAPP ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ c_Lazy__Sequence_Ohb__not__seq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).
thf(9804,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_New__DSequence_Opos__not__seq @ hAPP ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ c_Lazy__Sequence_Ohb__not__seq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(3511,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
thf(18545,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3511]) ).
thf(158,axiom,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Nat__Transfer_Otransfer__morphism ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__morphism__nat__int) ).
thf(5270,plain,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Nat__Transfer_Otransfer__morphism ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__of__nat) ).
thf(4796,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4797,plain,
! [B: $i,A: $i] :
( ( ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
| ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Oring__1 ) )
& ( ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Oring__1 ) ) ),
inference(cnf,[status(esa)],[4796]) ).
thf(4798,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Oring__1 ) ),
inference(cnfConj,[status(thm)],[4797]) ).
thf(4800,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Oring__1 )
| ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4798]) ).
thf(42872,plain,
! [B: $i,A: $i] :
( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Oring__1 )
| ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ) ),
inference(rewrite,[status(thm)],[4800,7678]) ).
thf(3057,axiom,
( ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).
thf(16761,plain,
( ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3057]) ).
thf(2630,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_OremoveAll ) )
= ( A @ ( c_fequal @ hAPP ) @ ( c_fNot @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Ofilter ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll__filter__not__eq) ).
thf(15078,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_OremoveAll ) )
= ( A @ ( c_fequal @ hAPP ) @ ( c_fNot @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Ofilter ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2630]) ).
thf(3243,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) )
<=> ( A @ ( B @ ( A @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__union__merge) ).
thf(17462,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( A @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3243]) ).
thf(844,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Otranspose__rel @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Otranspose ) )
= ( A @ ( B @ c_List_Otranspose ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I2_J) ).
thf(7962,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Otranspose__rel @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Otranspose ) )
= ( A @ ( B @ c_List_Otranspose ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(3757,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Big__Operators_Osemilattice__big ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( C @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).
thf(19551,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Big__Operators_Osemilattice__big ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( C @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3757]) ).
thf(2665,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__anti__mono) ).
thf(15211,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2665]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( G @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
<=> ( ( A @ ( C @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
& ( B @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__Cons) ).
thf(5423,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( A @ ( C @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
& ( B @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( G @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) ) )
& ( ( A @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( G @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
=> ( ( A @ ( C @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
& ( B @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( G @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( A @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
<=> ( ( A @ ( B @ ( C @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
& ( D @ ( F @ ( C @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__append) ).
thf(4974,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( G @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( ( ( A @ ( B @ ( C @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
& ( D @ ( F @ ( C @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) ) )
=> ( A @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) ) )
& ( ( A @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
& ( D @ ( F @ ( C @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(3844,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__insert) ).
thf(19918,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3844]) ).
thf(2732,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2__not__zero) ).
thf(15454,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2732]) ).
thf(2929,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__def) ).
thf(16232,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2929]) ).
thf(1800,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( C @ ( B @ c_List_Obutlast ) @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( A @ ( B @ c_List_Obutlast ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__append) ).
thf(11715,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( C @ ( B @ c_List_Obutlast ) @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( A @ ( B @ c_List_Obutlast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1800]) ).
thf(4016,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_List_Olistrel1 ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
thf(20513,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_List_Olistrel1 ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4016]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).
thf(5345,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(3114,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR1) ).
thf(16968,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3114]) ).
thf(2653,axiom,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I2_J) ).
thf(15156,plain,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2653]) ).
thf(914,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ ( tc_Code__Numeral_Ocode__numeral @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) @ ( C @ ( A @ ( B @ c_Random_Opick ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick__member) ).
thf(8223,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ ( tc_Code__Numeral_Ocode__numeral @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Osnd ) @ ( B @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) @ ( C @ ( A @ ( B @ c_Random_Opick ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(2523,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nth__imp__all__set) ).
thf(14629,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2523]) ).
thf(2774,axiom,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ c_Nat__Transfer_Onat__set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).
thf(15606,plain,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ c_Nat__Transfer_Onat__set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2774]) ).
thf(3795,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Oone__class_Oone @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__distrib) ).
thf(19707,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Oone__class_Oone @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3795]) ).
thf(1477,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(10413,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(4137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] : ( A @ ( B @ ( E @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__subset) ).
thf(21034,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] : ( A @ ( B @ ( E @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4137]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(6955,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(2582,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__less__iff__conj) ).
thf(14866,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2582]) ).
thf(1644,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).
thf(11096,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).
thf(3526,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).
thf(18586,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3526]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oremdups ) @ ( B @ ( C @ c_List_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_List_Oinsert ) ) @ ( C @ c_List_Oremdups ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__remdups) ).
thf(6459,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oremdups ) @ ( B @ ( C @ c_List_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_List_Oinsert ) ) @ ( C @ c_List_Oremdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1322,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
thf(9773,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(2025,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
thf(12546,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2025]) ).
thf(2457,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
thf(14353,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2457]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( c_Int_Onat @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__number__of__Suc) ).
thf(7389,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( c_Int_Onat @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( C @ ( B @ c_List_Obutlast ) @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).
thf(7481,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( C @ ( B @ c_List_Obutlast ) @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(3272,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).
thf(17578,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3272]) ).
thf(1272,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__pos) ).
thf(9608,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__eq) ).
thf(5577,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(4485,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).
thf(22368,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4485]) ).
thf(4038,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I13_J) ).
thf(20597,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4038]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__less__0__iff) ).
thf(4789,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4664,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).
thf(23049,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4664]) ).
thf(4295,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( D @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).
thf(21673,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( D @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4295]) ).
thf(1622,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).
thf(11007,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622]) ).
thf(2676,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(15248,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2676]) ).
thf(3191,axiom,
! [A: $i] :
~ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__zle__0__negative) ).
thf(17264,plain,
! [A: $i] :
~ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3191]) ).
thf(3547,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( B @ ( A @ c_List_Oset @ hAPP ) @ ( B @ ( A @ c_List_Olast ) @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__in__set) ).
thf(18696,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( B @ ( A @ c_List_Oset @ hAPP ) @ ( B @ ( A @ c_List_Olast ) @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3547]) ).
thf(1235,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__eq__power2) ).
thf(9444,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(2468,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
thf(14398,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2468]) ).
thf(812,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I3_J) ).
thf(7838,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(2343,axiom,
! [A: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ c_Set_Oinsert @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( A @ ( c_Int_ORep__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_Othe__elem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__def) ).
thf(13825,plain,
! [A: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ c_Set_Oinsert @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( A @ ( c_Int_ORep__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_Othe__elem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2343]) ).
thf(407,axiom,
c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Wellfounded_Owf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
thf(6235,plain,
c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Wellfounded_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ c_Int_Osucc )
= ( A @ c_Int_Osucc @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Bit1) ).
thf(4845,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 @ c_Int_Osucc )
= ( A @ c_Int_Osucc @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(2543,axiom,
! [A: $i] :
( ( A @ c_Relation_OId @ ( A @ ( A @ c_Relation_ORange ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id) ).
thf(14725,plain,
! [A: $i] :
( ( A @ c_Relation_OId @ ( A @ ( A @ c_Relation_ORange ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2543]) ).
thf(1633,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__number__of__eq__0) ).
thf(11057,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__num) ).
thf(8014,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(744,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nitpick_Oint__gcd @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ c_Nitpick_Onat__gcd ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oint__gcd__def) ).
thf(7610,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nitpick_Oint__gcd @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ c_Nitpick_Onat__gcd ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(4270,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( D @ ( E @ c_Relation_Oconverse ) @ hAPP ) @ ( A @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__converse__eq) ).
thf(21577,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_Relation_Oconverse ) @ hAPP ) @ ( A @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( E @ c_Relation_Oconverse ) @ hAPP ) @ ( A @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4270]) ).
thf(3302,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(17687,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3302]) ).
thf(3471,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oremove1 ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) )
& ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oremove1 ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remove1) ).
thf(18379,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oremove1 ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) )
& ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oremove1 ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3471]) ).
thf(4027,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
thf(20553,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4027]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ c_Divides_Opdivmod ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ c_Divides_OposDivAlg ) ) ) )
& ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ c_Divides_Opdivmod ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__posDivAlg) ).
thf(5583,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ c_Divides_Opdivmod ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ c_Divides_OposDivAlg ) ) ) )
& ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ c_Divides_Opdivmod ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(3132,axiom,
! [A: $i,B: $i,C: $i] :
( C
!= ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self) ).
thf(17042,plain,
! [A: $i,B: $i,C: $i] :
( C
!= ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3132]) ).
thf(2455,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__0L) ).
thf(14348,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2455]) ).
thf(3997,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Otranspose ) )
= ( A @ ( B @ c_List_Otranspose ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I2_J) ).
thf(20448,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Otranspose ) )
= ( A @ ( B @ c_List_Otranspose ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3997]) ).
thf(3476,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) ) )
=> ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
thf(18404,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) ) )
=> ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3476]) ).
thf(2559,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__trancl) ).
thf(14783,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2559]) ).
thf(2133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ ( G @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( G @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ ( G @ tc_prod ) @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib2) ).
thf(12950,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ ( G @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( G @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ ( G @ tc_prod ) @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2133]) ).
thf(4612,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( B
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__empty) ).
thf(22845,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( B
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( B
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4612]) ).
thf(2578,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).
thf(14855,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2578]) ).
thf(1727,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Divides_OnegateSnd @ hAPP ) @ ( B @ ( C @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__neg) ).
thf(11435,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Divides_OnegateSnd @ hAPP ) @ ( B @ ( C @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727]) ).
thf(1421,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_List_Oreplicate ) ) )
= ( A @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( A @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__add) ).
thf(10152,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_List_Oreplicate ) ) )
= ( A @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( A @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(2358,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
<=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def) ).
thf(13872,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) ) )
& ( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2358]) ).
thf(2734,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__0R) ).
thf(15466,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2734]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I35_J) ).
thf(4930,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(4439,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).
thf(22209,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4439]) ).
thf(4068,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_FunDef_Oreduction__pair ) )
<=> ( ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Ofst ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pair__def) ).
thf(20710,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Ofst ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) )
=> ( A @ ( B @ c_FunDef_Oreduction__pair ) ) )
& ( ( A @ ( B @ c_FunDef_Oreduction__pair ) )
=> ( ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Ofst ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4068]) ).
thf(2659,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Relation_OField @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Field) ).
thf(15189,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Relation_OField @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2659]) ).
thf(2573,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThan) ).
thf(14840,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2573]) ).
thf(3248,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I1_J) ).
thf(17491,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3248]) ).
thf(2641,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__IntI) ).
thf(15114,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2641]) ).
thf(3955,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( E @ ( A @ ( B @ ( H @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( H @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ ( B @ ( H @ ( C @ c_Fun_Obij__betw ) ) ) ) )
<=> ( D @ ( A @ ( B @ ( F @ ( C @ ( G @ ( H @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( G @ ( C @ c_Fun_Obij__betw ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__comp__iff2) ).
thf(20316,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( E @ ( A @ ( B @ ( H @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( H @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( D @ ( A @ ( B @ ( F @ ( C @ ( G @ ( H @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( G @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( E @ ( A @ ( B @ ( H @ ( C @ c_Fun_Obij__betw ) ) ) ) ) )
& ( ( E @ ( A @ ( B @ ( H @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( D @ ( A @ ( B @ ( F @ ( C @ ( G @ ( H @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( G @ ( C @ c_Fun_Obij__betw ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3955]) ).
thf(568,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__code__numeral__def) ).
thf(6941,plain,
! [A: $i,B: $i] :
( ( ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(3266,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
<=> ( ~ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__insert) ).
thf(17550,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ~ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) )
=> ( A @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) )
& ( ( A @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ~ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3266]) ).
thf(2168,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
thf(13099,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2168]) ).
thf(4319,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ hAPP ) @ hBOOL ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Set_OCollect @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Set_OCollect @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__cong) ).
thf(21771,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( A @ hAPP ) @ hBOOL )
=> ( C @ ( B @ hAPP ) @ hBOOL ) )
& ( ( C @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Set_OCollect @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Set_OCollect @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4319]) ).
thf(378,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).
thf(6108,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(6109,plain,
~ ? [A: $i] :
( ( A @ c_Int_OBit0 )
= c_Int_OMin ),
inference(miniscope,[status(thm)],[6108]) ).
thf(6110,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
inference(cnf,[status(esa)],[6109]) ).
thf(6111,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
inference(lifteq,[status(thm)],[6110]) ).
thf(1388,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_OtakeWhile ) ) )
= ( A @ ( B @ ( D @ c_List_OtakeWhile ) ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__append2) ).
thf(10021,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_OtakeWhile ) ) )
= ( A @ ( B @ ( D @ c_List_OtakeWhile ) ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(46,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Divides_Odivmod__nat ) @ ( A @ ( B @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).
thf(4883,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Divides_Odivmod__nat ) @ ( A @ ( B @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1910,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).
thf(12142,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1910]) ).
thf(2654,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(15157,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2654]) ).
thf(4598,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty) ).
thf(22795,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4598]) ).
thf(1558,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( ( ~ ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).
thf(10771,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( ( ~ ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558]) ).
thf(4424,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).
thf(22154,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4424]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ c_List_Oset @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_OdropWhile ) ) )
= ( A @ ( C @ ( B @ ( E @ c_List_OdropWhile ) ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__append1) ).
thf(8149,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ c_List_Oset @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_OdropWhile ) ) )
= ( A @ ( C @ ( B @ ( E @ c_List_OdropWhile ) ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(4559,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( D @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
thf(22642,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( D @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4559]) ).
thf(1665,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( A @ c_List_Olist_ONil @ ( A @ c_List_Olinorder__class_Osorted ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_ONil) ).
thf(11189,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( A @ c_List_Olist_ONil @ ( A @ c_List_Olinorder__class_Osorted ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).
thf(3555,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i,G: $i] :
( ( ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( G @ ( F @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( G @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__fold1SetE) ).
thf(18745,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i,G: $i] :
( ( ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( G @ ( F @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( G @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3555]) ).
thf(2131,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
thf(12945,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2131]) ).
thf(2853,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oremove) ).
thf(15930,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2853]) ).
thf(1018,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rotate) ).
thf(8572,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(39032,plain,
~ ( c_Int_OPls @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
inference(rewrite,[status(thm)],[15292,7678]) ).
thf(45346,plain,
( ( ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
!= ( c_Int_OPls @ ( c_Nat__Numeral_Oneg @ hAPP ) ) )
| ~ ( c_Int_OPls @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[8226,39032]) ).
thf(45670,plain,
( ( c_Int_OPls != c_Int_OPls )
| ( ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus )
!= c_Nat__Numeral_Oneg )
| ~ ( c_Int_OPls @ hBOOL ) ),
inference(simp,[status(thm)],[45346]) ).
thf(45752,plain,
( ( ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus )
!= c_Nat__Numeral_Oneg )
| ~ ( c_Int_OPls @ hBOOL ) ),
inference(simp,[status(thm)],[45670]) ).
thf(4322,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(21797,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4322]) ).
thf(4628,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) )
<=> ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I1_J) ).
thf(22899,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) )
=> ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4628]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__add) ).
thf(7874,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(2772,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).
thf(15599,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2772]) ).
thf(802,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(7809,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Osplice ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__splice) ).
thf(5687,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Osplice ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(2687,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__sup__iff) ).
thf(15281,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2687]) ).
thf(1534,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( C @ ( A @ ( B @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__map) ).
thf(10678,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( C @ ( A @ ( B @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(3359,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( ( A @ ( B @ hAPP ) @ ( A @ ( B @ hAPP ) @ ( C @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).
thf(17898,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( ( A @ ( B @ hAPP ) @ ( A @ ( B @ hAPP ) @ ( C @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3359]) ).
thf(4134,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
thf(21026,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4134]) ).
thf(2595,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [F: $i] :
( ( C @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__iff) ).
thf(14908,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( C @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( C @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2595]) ).
thf(1533,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__zipI1) ).
thf(10676,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).
thf(1396,axiom,
c_FunDef_Opair__less @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Owf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pair__less) ).
thf(10052,plain,
c_FunDef_Opair__less @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(4363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__empty) ).
thf(21951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4363]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
thf(5951,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_List_Oupt ) @ ( C @ ( tc_Nat_Onat @ c_List_Olist__all ) ) )
<=> ( A @ ( B @ ( C @ c_List_Oall__interval__nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__iff__all__interval__nat) ).
thf(6218,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Oall__interval__nat ) ) )
=> ( A @ ( B @ c_List_Oupt ) @ ( C @ ( tc_Nat_Onat @ c_List_Olist__all ) ) ) )
& ( ( A @ ( B @ c_List_Oupt ) @ ( C @ ( tc_Nat_Onat @ c_List_Olist__all ) ) )
=> ( A @ ( B @ ( C @ c_List_Oall__interval__nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(4666,axiom,
tc_HOL_Obool @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
thf(23055,plain,
tc_HOL_Obool @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4666]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate ) )
= ( B @ c_List_Orotate1 @ ( A @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__def) ).
thf(4817,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate ) )
= ( B @ c_List_Orotate1 @ ( A @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__left) ).
thf(4898,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(3693,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [E: $i] :
( ( D @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) )
=> ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Inter) ).
thf(19287,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [E: $i] :
( ( D @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) )
=> ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3693]) ).
thf(3671,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Inter) ).
thf(19186,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3671]) ).
thf(3772,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Finite__Set_Ofold ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__def) ).
thf(19620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Finite__Set_Ofold ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3772]) ).
thf(1259,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__odd) ).
thf(9530,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(1075,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update__eq) ).
thf(8792,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(3638,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
thf(19070,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3638]) ).
thf(2241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( C @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Equiv__Relations_Ocongruent ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruentI) ).
thf(13394,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( C @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Equiv__Relations_Ocongruent ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2241]) ).
thf(900,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc__number__of) ).
thf(8176,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(2890,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
thf(16068,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2890]) ).
thf(4076,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omax @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).
thf(20754,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omax @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4076]) ).
thf(3981,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(20402,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3981]) ).
thf(1752,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ c_Nat__Transfer_Ois__nat ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( c_Int_Onat @ ( C @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).
thf(11536,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ c_Nat__Transfer_Ois__nat ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( c_Int_Onat @ ( C @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752]) ).
thf(2333,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oin__idem) ).
thf(13790,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2333]) ).
thf(3837,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff) ).
thf(19879,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3837]) ).
thf(827,axiom,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__nat__eq) ).
thf(7898,plain,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(3975,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__conj) ).
thf(20380,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3975]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(7091,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(2475,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__iff) ).
thf(14437,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2475]) ).
thf(1054,axiom,
! [A: $i] :
( ( A @ class_Lattices_Oab__semigroup__idem__mult )
=> ( A @ c_Groups_Otimes__class_Otimes @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem) ).
thf(8704,plain,
! [A: $i] :
( ( A @ class_Lattices_Oab__semigroup__idem__mult )
=> ( A @ c_Groups_Otimes__class_Otimes @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(1816,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zminus__int) ).
thf(11782,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1816]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Opartition ) ) )
= ( A @ ( C @ ( D @ c_List_Opartition ) ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_If @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ c_COMBS ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).
thf(8631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Opartition ) ) )
= ( A @ ( C @ ( D @ c_List_Opartition ) ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_If @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ c_COMBS ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(2820,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( B @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( F @ ( A @ hAPP ) @ ( G @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
!= ( G @ ( F @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE) ).
thf(15798,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( B @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( F @ ( A @ hAPP ) @ ( G @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
!= ( G @ ( F @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2820]) ).
thf(1656,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
thf(11157,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1656]) ).
thf(3934,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__semigroup__mult )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__insert) ).
thf(20248,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__semigroup__mult )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3934]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_Opred @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__pred) ).
thf(5166,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_Opred @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(3250,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
thf(17503,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3250]) ).
thf(4283,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__semigroup__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__eq__fold) ).
thf(21632,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__semigroup__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4283]) ).
thf(3356,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un) ).
thf(17890,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3356]) ).
thf(3080,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(16847,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3080]) ).
thf(2908,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add) ).
thf(16147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2908]) ).
thf(1541,axiom,
! [A: $i] :
( ( c_Int_OMin
= ( A @ c_Int_OBit1 ) )
<=> ( c_Int_OMin = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).
thf(10701,plain,
! [A: $i] :
( ( ( c_Int_OMin = A )
=> ( c_Int_OMin
= ( A @ c_Int_OBit1 ) ) )
& ( ( c_Int_OMin
= ( A @ c_Int_OBit1 ) )
=> ( c_Int_OMin = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541]) ).
thf(10702,plain,
( ! [A: $i] :
( ( c_Int_OMin = A )
=> ( c_Int_OMin
= ( A @ c_Int_OBit1 ) ) )
& ! [A: $i] :
( ( c_Int_OMin
= ( A @ c_Int_OBit1 ) )
=> ( c_Int_OMin = A ) ) ),
inference(miniscope,[status(thm)],[10701]) ).
thf(10703,plain,
! [B: $i,A: $i] :
( ( ( c_Int_OMin
= ( B @ c_Int_OBit1 ) )
| ( c_Int_OMin != B ) )
& ( ( c_Int_OMin = A )
| ( c_Int_OMin
!= ( A @ c_Int_OBit1 ) ) ) ),
inference(cnf,[status(esa)],[10702]) ).
thf(10705,plain,
! [A: $i] :
( ( c_Int_OMin
= ( A @ c_Int_OBit1 ) )
| ( c_Int_OMin != A ) ),
inference(cnfConj,[status(thm)],[10703]) ).
thf(10707,plain,
! [A: $i] :
( ( ( A @ c_Int_OBit1 )
= c_Int_OMin )
| ( c_Int_OMin != A ) ),
inference(lifteq,[status(thm)],[10705]) ).
thf(10708,plain,
( ( c_Int_OMin @ c_Int_OBit1 )
= c_Int_OMin ),
inference(simp,[status(thm)],[10707]) ).
thf(2869,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( C @ c_List_Olistrel ) @ ( B @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).
thf(15987,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( C @ c_List_Olistrel ) @ ( B @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2869]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__assoc) ).
thf(6518,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(23943,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,23909]) ).
thf(23944,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[23943]) ).
thf(23945,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[23944:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(23986,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[23945]) ).
thf(24000,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4741,23986]) ).
thf(24018,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[24000]) ).
thf(24030,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[24018]) ).
thf(27801,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,24030]) ).
thf(27802,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[27801]) ).
thf(27803,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[27802:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(27887,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[27803]) ).
thf(39022,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(rewrite,[status(thm)],[27887,7678]) ).
thf(2360,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(13883,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2360]) ).
thf(4310,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( D @ c_List_Oremove1 ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__set__remove1) ).
thf(21727,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( D @ c_List_Oremove1 ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4310]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__append) ).
thf(8105,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(3726,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_OCons) ).
thf(19425,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3726]) ).
thf(2698,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__imp__bij__inv) ).
thf(15312,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2698]) ).
thf(1577,axiom,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__0) ).
thf(10830,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577]) ).
thf(4340,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
thf(21858,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4340]) ).
thf(2480,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
thf(14456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2480]) ).
thf(2843,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastLessThan) ).
thf(15882,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2843]) ).
thf(4386,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__is__Un) ).
thf(22039,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4386]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_List_Oconcat ) )
= ( A @ ( C @ c_List_Oconcat ) ) )
=> ( ( ( B @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ! [D: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( D @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__injective) ).
thf(6428,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_List_Oconcat ) )
= ( A @ ( C @ c_List_Oconcat ) ) )
=> ( ( ( B @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ! [D: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( D @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(1364,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OposDivAlg ) )
= ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OposDivAlg ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OposDivAlg ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn__number__of) ).
thf(9910,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OposDivAlg ) )
= ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OposDivAlg ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OposDivAlg ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(858,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__split) ).
thf(8017,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(2305,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union2) ).
thf(13682,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2305]) ).
thf(3455,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ c_List_Otake @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ ( tc_Nat_Onat @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist_ONil @ ( D @ tc_List_Olist @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons) ).
thf(18306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ c_List_Otake @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ ( tc_Nat_Onat @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist_ONil @ ( D @ tc_List_Olist @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3455]) ).
thf(4581,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) )
= ( A @ c_Set_OBex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__bool__eq) ).
thf(22736,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) )
= ( A @ c_Set_OBex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4581]) ).
thf(1226,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__number__of) ).
thf(9397,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(2508,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__assoc) ).
thf(14566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2508]) ).
thf(1111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ c_List_Olist_ONil )
= ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__map__conv) ).
thf(8938,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( C @ c_List_Olist_ONil ) )
=> ( ( D @ c_List_Olist_ONil )
= ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ c_List_Olist_ONil )
= ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
=> ( A
= ( C @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(4462,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
thf(22288,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4462]) ).
thf(130,axiom,
tc_Int_Oint @ class_Int_Onumber__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
thf(5181,plain,
tc_Int_Oint @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I10_J) ).
thf(5080,plain,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
thf(7054,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(1286,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( E @ ( F @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ ( F @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__unfold) ).
thf(9667,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( E @ ( F @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ ( F @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(3651,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
thf(19114,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3651]) ).
thf(2219,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Ohd @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__replicate) ).
thf(13308,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Ohd @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2219]) ).
thf(3845,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( D @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
thf(19921,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( D @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3845]) ).
thf(4479,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oempty) ).
thf(22343,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4479]) ).
thf(2634,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(15089,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2634]) ).
thf(3279,axiom,
! [A: $i,B: $i] : ( B @ c_Relation_OId @ ( A @ ( A @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdI) ).
thf(17619,plain,
! [A: $i,B: $i] : ( B @ c_Relation_OId @ ( A @ ( A @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3279]) ).
thf(3505,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( B @ hAPP ) @ ( D @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__diff__distrib) ).
thf(18512,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( B @ hAPP ) @ ( D @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3505]) ).
thf(923,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__int) ).
thf(8251,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(2449,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oin__idem) ).
thf(14313,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2449]) ).
thf(4522,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__empty) ).
thf(22511,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4522]) ).
thf(1878,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__supI1) ).
thf(12019,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1878]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Oring__1 )
& ( D @ class_Groups_Ocomm__monoid__mult ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( D @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( D @ c_Int_Oring__1__class_Oof__int @ ( C @ ( D @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__setprod) ).
thf(4770,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Oring__1 )
& ( D @ class_Groups_Ocomm__monoid__mult ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( D @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( D @ c_Int_Oring__1__class_Oof__int @ ( C @ ( D @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4771,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( D @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( D @ c_Int_Oring__1__class_Oof__int @ ( C @ ( D @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) )
| ~ ( D @ class_Rings_Oring__1 )
| ~ ( D @ class_Groups_Ocomm__monoid__mult ) ),
inference(cnf,[status(esa)],[4770]) ).
thf(4772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ class_Rings_Oring__1 )
| ~ ( D @ class_Groups_Ocomm__monoid__mult )
| ( ( A @ ( B @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( D @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( D @ c_Int_Oring__1__class_Oof__int @ ( C @ ( D @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4771]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).
thf(6593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(1385,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).
thf(10015,plain,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(3891,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
thf(20092,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3891]) ).
thf(2857,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( G @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__anti__mono) ).
thf(15944,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( G @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2857]) ).
thf(3063,axiom,
! [A: $i] :
( ( A @ c_Relation_OId @ ( A @ ( A @ c_Relation_ODomain ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id) ).
thf(16786,plain,
! [A: $i] :
( ( A @ c_Relation_OId @ ( A @ ( A @ c_Relation_ODomain ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3063]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( A @ ( B @ c_List_Olast ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__append) ).
thf(7111,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( A @ ( B @ c_List_Olast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(1773,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__curry) ).
thf(11625,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773]) ).
thf(2063,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__mono) ).
thf(12696,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2063]) ).
thf(1739,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_COMBI @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__number__of__odd) ).
thf(11496,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_COMBI @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739]) ).
thf(1556,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Nat_Onat_Onat__rec ) ) @ ( tc_Int_Oint @ ( E @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ ( E @ ( E @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( E @ c_If @ ( tc_Int_Oint @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( E @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__add__eq__if) ).
thf(10761,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Nat_Onat_Onat__rec ) ) @ ( tc_Int_Oint @ ( E @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ ( E @ ( E @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( E @ c_If @ ( tc_Int_Oint @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( E @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556]) ).
thf(3449,axiom,
! [A: $i] :
( ( A @ c_Wellfounded_Ofinite__psubset )
= ( A @ c_Finite__Set_Ofinite @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless @ ( c_fconj @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBS ) ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__psubset__def) ).
thf(18287,plain,
! [A: $i] :
( ( A @ c_Wellfounded_Ofinite__psubset )
= ( A @ c_Finite__Set_Ofinite @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless @ ( c_fconj @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBS ) ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3449]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).
thf(6363,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(3078,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I3_J) ).
thf(16832,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3078]) ).
thf(1469,axiom,
! [A: $i] :
( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Osucc @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__number__of) ).
thf(10381,plain,
! [A: $i] :
( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Osucc @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(1300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upd__conv__take__nth__drop) ).
thf(9714,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(1811,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I25_J) ).
thf(11757,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1811]) ).
thf(1232,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__nat__eq__int__zless) ).
thf(9426,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) )
=> ( B @ ( A @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( F @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__takeI) ).
thf(5620,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) )
=> ( B @ ( A @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( F @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(3210,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I16_J) ).
thf(17345,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3210]) ).
thf(1456,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
thf(10342,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(2420,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).
thf(14153,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2420]) ).
thf(2186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [G: $i] :
( ( F @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) ) )
=> ( A @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__INTER) ).
thf(13190,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [G: $i] :
( ( F @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) ) )
=> ( A @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2186]) ).
thf(4455,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( tc_HOL_Obool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( B @ ( c_fNot @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( c_fconj @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ c_COMBS ) ) @ ( E @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_LoopF) ).
thf(22265,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( tc_HOL_Obool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( B @ ( c_fNot @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( c_fconj @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ c_COMBS ) ) @ ( E @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4455]) ).
thf(2048,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(12639,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2048]) ).
thf(3110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__INFI__fold__inf) ).
thf(16958,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3110]) ).
thf(4253,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Rings_Odvd )
& ( E @ class_Groups_Ocomm__monoid__mult ) )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__dvd__setprod__subset) ).
thf(21514,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Rings_Odvd )
& ( E @ class_Groups_Ocomm__monoid__mult ) )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4253]) ).
thf(2079,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__flatten) ).
thf(12746,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2079]) ).
thf(3141,axiom,
! [A: $i] :
( ( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zsgn__def) ).
thf(17074,plain,
! [A: $i] :
( ( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3141]) ).
thf(3225,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__I) ).
thf(17402,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3225]) ).
thf(2778,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq) ).
thf(15619,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2778]) ).
thf(2615,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__int) ).
thf(15022,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2615]) ).
thf(2300,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
thf(13661,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2300]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__filter) ).
thf(5464,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(2232,axiom,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ( B @ ( A @ ( C @ c_List_Olist__ex ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bex__set__list__ex) ).
thf(13355,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ c_List_Olist__ex ) ) )
=> ? [D: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ? [D: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( C @ c_List_Olist__ex ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2232]) ).
thf(4638,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__empty) ).
thf(22952,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4638]) ).
thf(2964,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( D @ ( A @ ( E @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).
thf(16380,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( D @ ( A @ ( E @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( A @ ( E @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2964]) ).
thf(4099,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( ( ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ~ ( B @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
| ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__psubset__iff) ).
thf(20880,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( ( ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ~ ( B @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
| ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( ( ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ~ ( B @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
| ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4099]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__size ) ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__size__simp) ).
thf(8594,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__size ) ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(1531,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olexord ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olexord ) @ ( C @ ( A @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).
thf(10671,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olexord ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olexord ) @ ( C @ ( A @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531]) ).
thf(2742,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
thf(15495,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2742]) ).
thf(3875,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__antimono) ).
thf(20033,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3875]) ).
thf(1680,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__zip) ).
thf(11243,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680]) ).
thf(2410,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( c_fequal @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_HOL_OThe ) )
= ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_The__split__eq) ).
thf(14110,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( c_fequal @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_HOL_OThe ) )
= ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2410]) ).
thf(1352,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__greater) ).
thf(9878,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(2994,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Osubset__idem) ).
thf(16524,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2994]) ).
thf(1604,axiom,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__nat__number__of) ).
thf(10936,plain,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604]) ).
thf(3508,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitI) ).
thf(18521,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3508]) ).
thf(3885,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__fold__remove) ).
thf(20069,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3885]) ).
thf(4397,axiom,
! [A: $i] : ( A @ c_Wellfounded_Ofinite__psubset @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__finite__psubset) ).
thf(22072,plain,
! [A: $i] : ( A @ c_Wellfounded_Ofinite__psubset @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4397]) ).
thf(2383,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) )
= A )
<=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__all__conv) ).
thf(13964,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) )
= A ) )
& ( ( ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) )
= A )
=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2383]) ).
thf(2580,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__f__f) ).
thf(14861,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2580]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__minus) ).
thf(4742,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4743,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( B @ class_Rings_Oring__1 ) ),
inference(cnf,[status(esa)],[4742]) ).
thf(4744,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Rings_Oring__1 )
| ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4743]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(8132,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(16717,plain,
( ( c_Com_Ocom_OSKIP @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[16716]) ).
thf(43846,plain,
( ( c_Com_Ocom_OSKIP @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Orderings_Obot__class_Obot ) ),
inference(rewrite,[status(thm)],[16717,20483]) ).
thf(2098,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I11_J) ).
thf(12803,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2098]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__in__listsp__conv) ).
thf(6164,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__rev) ).
thf(5213,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(998,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_List_Oupt ) @ ( C @ ( tc_Nat_Onat @ c_List_Olist__ex ) ) )
<=> ~ ( A @ ( B @ ( C @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ c_List_Oall__interval__nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__iff__not__all__inverval__nat) ).
thf(8499,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( A @ ( B @ ( C @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ c_List_Oall__interval__nat ) ) )
=> ( A @ ( B @ c_List_Oupt ) @ ( C @ ( tc_Nat_Onat @ c_List_Olist__ex ) ) ) )
& ( ( A @ ( B @ c_List_Oupt ) @ ( C @ ( tc_Nat_Onat @ c_List_Olist__ex ) ) )
=> ~ ( A @ ( B @ ( C @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ c_List_Oall__interval__nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(4224,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Predicate_OPowp ) @ ( B @ ( C @ c_Predicate_OPowp ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__mono) ).
thf(21389,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Predicate_OPowp ) @ ( B @ ( C @ c_Predicate_OPowp ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4224]) ).
thf(2125,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__idem) ).
thf(12917,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2125]) ).
thf(2587,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__left) ).
thf(14882,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2587]) ).
thf(1153,axiom,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2__eq__if) ).
thf(9100,plain,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(1574,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(10823,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574]) ).
thf(1896,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( B @ c_COMBB ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( B @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( B @ ( D @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__image__set) ).
thf(12091,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( B @ c_COMBB ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( B @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( B @ ( D @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1896]) ).
thf(1785,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ ( B @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gauss__sum) ).
thf(11666,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ ( B @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785]) ).
thf(4589,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__singleton) ).
thf(22758,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4589]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(8968,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(2683,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).
thf(15270,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2683]) ).
thf(4662,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__single) ).
thf(23043,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4662]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ? [F: $i] :
( ( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
thf(6837,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ? [F: $i] :
( ( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(3152,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__caseI) ).
thf(17118,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3152]) ).
thf(577,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist__ex ) ) )
<=> ? [D: $i] :
( ( D @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__length) ).
thf(6978,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Olist__ex ) ) ) )
& ( ( A @ ( B @ ( C @ c_List_Olist__ex ) ) )
=> ? [D: $i] :
( ( D @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(3910,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).
thf(20165,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3910]) ).
thf(3811,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__E2) ).
thf(19764,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3811]) ).
thf(3542,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oless__than @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__than__iff) ).
thf(18672,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Wellfounded_Oless__than @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Wellfounded_Oless__than @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3542]) ).
thf(1508,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__int__eq) ).
thf(10539,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508]) ).
thf(2807,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq) ).
thf(15728,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2807]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append__length__plus) ).
thf(7806,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oconcat ) @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Ofilter ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Oconcat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__concat) ).
thf(7577,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oconcat ) @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Ofilter ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Oconcat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(4201,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oinsert ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__insert) ).
thf(21306,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oinsert ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4201]) ).
thf(2541,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Big__Operators_Olinorder__class_OMax ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Min__eq__Max) ).
thf(14719,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Big__Operators_Olinorder__class_OMax ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2541]) ).
thf(1627,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( D @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__swap1) ).
thf(11026,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( D @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627]) ).
thf(2757,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I45_J) ).
thf(15550,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2757]) ).
thf(699,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Ois__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).
thf(7404,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Ois__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(2883,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
thf(16036,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2883]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mod) ).
thf(6625,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_OtakeWhile ) ) )
= ( A @ ( B @ ( D @ ( C @ ( tc_HOL_Obool @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_OtakeWhile ) ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__map) ).
thf(6275,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_OtakeWhile ) ) )
= ( A @ ( B @ ( D @ ( C @ ( tc_HOL_Obool @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_OtakeWhile ) ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rev) ).
thf(4814,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(2415,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(14131,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2415]) ).
thf(566,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).
thf(6935,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(3181,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
thf(17239,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3181]) ).
thf(1970,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( D @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL2) ).
thf(12357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( D @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1970]) ).
thf(2725,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ c_List_Oreplicate ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__0) ).
thf(15421,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ c_List_Oreplicate ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2725]) ).
thf(2827,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
thf(15830,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2827]) ).
thf(763,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( A @ c_List_Olist_ONil @ ( A @ c_List_Olinorder__class_Osorted ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_Oequations_I1_J) ).
thf(7682,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( A @ c_List_Olist_ONil @ ( A @ c_List_Olinorder__class_Osorted ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(1114,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(8952,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__nat) ).
thf(4736,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(894,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( F @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ ( C @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( F @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ ( D @ ( F @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_update__zip) ).
thf(8159,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( F @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ ( C @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( F @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ ( D @ ( F @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(2044,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Ounion__idem) ).
thf(12622,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2044]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power) ).
thf(8230,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(668,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).
thf(7293,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(2833,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( D @ c_Finite__Set_Ocard @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__same__card) ).
thf(15852,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( D @ c_Finite__Set_Ocard @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2833]) ).
thf(3256,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
thf(17518,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3256]) ).
thf(2275,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatMost ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
thf(13539,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OatMost ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatMost ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2275]) ).
thf(4238,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Opair__leq @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leqI1) ).
thf(21463,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Opair__leq @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4238]) ).
thf(4278,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oidem) ).
thf(21604,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4278]) ).
thf(2451,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__take__subset) ).
thf(14318,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2451]) ).
thf(3685,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olexord ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i,E: $i] :
( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).
thf(19241,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i,E: $i] :
( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( A @ ( C @ c_List_Olexord ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_List_Olexord ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i,E: $i] :
( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3685]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__int__eq) ).
thf(4802,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4803,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(cnf,[status(esa)],[4802]) ).
thf(4804,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(lifteq,[status(thm)],[4803]) ).
thf(2083,axiom,
! [A: $i] :
( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I1_J) ).
thf(12756,plain,
! [A: $i] :
( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2083]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
thf(7668,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(6248,plain,
( ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[6247]) ).
thf(45854,plain,
( ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Orderings_Obot__class_Obot ) ),
inference(rewrite,[status(thm)],[6248,20483]) ).
thf(4214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converseD) ).
thf(21345,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4214]) ).
thf(4487,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
=> ( tc_HOL_Obool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_fNot @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Loop__sound__lemma) ).
thf(22375,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
=> ( tc_HOL_Obool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_fNot @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4487]) ).
thf(1988,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__strict__subset__iff) ).
thf(12418,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1988]) ).
thf(3818,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(19790,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3818]) ).
thf(840,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__3) ).
thf(7948,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1220,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__drop__conv__nth) ).
thf(9365,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(2765,axiom,
c_FunDef_Omin__weak @ ( c_FunDef_Omin__strict @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_FunDef_Oreduction__pair ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__rpair__set) ).
thf(15582,plain,
c_FunDef_Omin__weak @ ( c_FunDef_Omin__strict @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_FunDef_Oreduction__pair ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2765]) ).
thf(1985,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Enum_Oenum )
& ( B @ class_Enum_Oenum ) )
=> ( A @ ( B @ tc_sum ) @ class_Enum_Oenum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Enum_Oenum) ).
thf(12410,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Enum_Oenum )
& ( B @ class_Enum_Oenum ) )
=> ( A @ ( B @ tc_sum ) @ class_Enum_Oenum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1985]) ).
thf(3239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( D @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key_Osimps_I1_J) ).
thf(17450,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( D @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3239]) ).
thf(4010,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(20493,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4010]) ).
thf(731,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) )
& ( ( F = E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(7544,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) )
& ( ( F = E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(912,axiom,
( ( c_Int_OPls @ c_Int_Opred )
= c_Int_OMin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Pls) ).
thf(8218,plain,
( ( c_Int_OPls @ c_Int_Opred )
= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(8219,plain,
( ( c_Int_OPls @ c_Int_Opred )
= c_Int_OMin ),
inference(lifteq,[status(thm)],[8218]) ).
thf(1218,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__if__abs__eq) ).
thf(9359,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(4258,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Image) ).
thf(21529,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4258]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( C @ ( E @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_Oconverse ) @ hAPP ) )
= ( B @ ( C @ ( E @ c_Relation_Oconverse ) @ hAPP ) @ ( A @ ( D @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( E @ ( C @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rel__comp) ).
thf(7340,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( C @ ( E @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_Oconverse ) @ hAPP ) )
= ( B @ ( C @ ( E @ c_Relation_Oconverse ) @ hAPP ) @ ( A @ ( D @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( E @ ( C @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(2605,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
thf(14950,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2605]) ).
thf(4166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD2) ).
thf(21155,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4166]) ).
thf(3628,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__power) ).
thf(19034,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3628]) ).
thf(3177,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(17229,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3177]) ).
thf(2003,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeI) ).
thf(12481,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2003]) ).
thf(2144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetI) ).
thf(12994,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2144]) ).
thf(4663,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).
thf(23046,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4663]) ).
thf(3018,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__left__commute) ).
thf(16605,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3018]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olist_ONil @ ( B @ ( C @ ( D @ c_List_Olist__all2 ) ) ) ) )
<=> ( A
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__Nil) ).
thf(5374,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( C @ c_List_Olist_ONil ) )
=> ( A @ ( D @ c_List_Olist_ONil @ ( B @ ( C @ ( D @ c_List_Olist__all2 ) ) ) ) ) )
& ( ( A @ ( D @ c_List_Olist_ONil @ ( B @ ( C @ ( D @ c_List_Olist__all2 ) ) ) ) )
=> ( A
= ( C @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
thf(6033,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(8326,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(3219,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono__zero__left) ).
thf(17377,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3219]) ).
thf(1632,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) )
= A )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__eqD) ).
thf(11052,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) )
= A )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632]) ).
thf(711,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ! [D: $i] :
( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__eq__iff__nth__eq) ).
thf(7463,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) )
=> ( C = B ) )
& ( ( C = B )
=> ( ! [D: $i] :
( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(3883,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__subset) ).
thf(20064,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3883]) ).
thf(1932,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I8_J) ).
thf(12218,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1932]) ).
thf(2180,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta) ).
thf(13169,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2180]) ).
thf(2461,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [H: $i] :
( ( D @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( H @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__iff) ).
thf(14369,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ! [H: $i] :
( ( D @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( H @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [H: $i] :
( ( D @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( H @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2461]) ).
thf(1562,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(10787,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).
thf(2095,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__Int) ).
thf(12795,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2095]) ).
thf(4139,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( A @ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le2) ).
thf(21038,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( A @ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4139]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(6999,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(2402,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__replicate__conv__if) ).
thf(14067,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2402]) ).
thf(3962,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Big__Operators_Olinorder__class_OMin ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Max__eq__Min) ).
thf(20335,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Big__Operators_Olinorder__class_OMin ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3962]) ).
thf(2288,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__least) ).
thf(13607,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2288]) ).
thf(1918,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
thf(12164,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1918]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I11_J) ).
thf(4970,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__diff) ).
thf(5639,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(1248,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).
thf(9498,plain,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(2773,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(15602,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2773]) ).
thf(2548,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( E @ c_COMBK ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_K__record__comp) ).
thf(14740,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( E @ c_COMBK ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2548]) ).
thf(3762,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(19579,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3762]) ).
thf(2018,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ounion__inter) ).
thf(12518,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2018]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Olast ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__conv__nth) ).
thf(7221,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Olast ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(4438,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
thf(22201,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) )
& ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4438]) ).
thf(3125,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__atMost__Suc) ).
thf(17022,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3125]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) )
= ( A @ ( C @ c_List_Otl @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__take) ).
thf(5900,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) )
= ( A @ ( C @ c_List_Otl @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(1357,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).
thf(9893,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult2) ).
thf(6207,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( A @ ( C @ ( B @ ( D @ ( D @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_Finite__Set_Ofun__left__comm ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).
thf(7169,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( A @ ( C @ ( B @ ( D @ ( D @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_Finite__Set_Ofun__left__comm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Otl @ hAPP ) @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__tl) ).
thf(7587,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Otl @ hAPP ) @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(2900,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__nat__conj) ).
thf(16112,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2900]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F = E )
=> ( ( F @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(5973,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F = E )
=> ( ( F @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ c_List_Ofoldr ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr1) ).
thf(5498,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ c_List_Ofoldr ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(4071,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
thf(20733,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4071]) ).
thf(4186,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( ( A @ ( C @ c_Relation_Osym ) )
=> ( ( A @ ( C @ c_Relation_Otrans ) )
=> ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivI) ).
thf(21246,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( ( A @ ( C @ c_Relation_Osym ) )
=> ( ( A @ ( C @ c_Relation_Otrans ) )
=> ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4186]) ).
thf(1886,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Oreplicate ) ) @ ( C @ ( D @ ( F @ c_List_Oreplicate ) ) @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__replicate) ).
thf(12059,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Oreplicate ) ) @ ( C @ ( D @ ( F @ c_List_Oreplicate ) ) @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1886]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult1__eq) ).
thf(7069,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(4254,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).
thf(21516,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4254]) ).
thf(1423,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [E: $i,F: $i] :
( ( B
= ( E @ ( F @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) )
& ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( F @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( E @ ( F @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__iff__update) ).
thf(10158,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i,F: $i] :
( ( B
= ( E @ ( F @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) )
& ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( F @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( E @ ( F @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i,F: $i] :
( ( B
= ( E @ ( F @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) )
& ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( F @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( E @ ( F @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423]) ).
thf(3759,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) )
<=> ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).
thf(19562,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) )
=> ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3759]) ).
thf(3927,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI1) ).
thf(20229,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3927]) ).
thf(4120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( B @ ( F @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( D @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__inv__into__eq) ).
thf(20967,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( B @ ( F @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( D @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4120]) ).
thf(3849,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] : ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__iff) ).
thf(19943,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] : ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3849]) ).
thf(2628,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__upto) ).
thf(15069,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2628]) ).
thf(2760,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( F @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( H @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( D @ ( E @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__I) ).
thf(15560,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( F @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( H @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( D @ ( E @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2760]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev) ).
thf(4829,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(4185,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__restrict__set_H) ).
thf(21243,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4185]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Divides_OnegDivAlg ) )
= ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Divides_OnegDivAlg ) @ ( B @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Divides_OnegDivAlg ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn) ).
thf(4934,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Divides_OnegDivAlg ) )
= ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Divides_OnegDivAlg ) @ ( B @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Divides_OnegDivAlg ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(3632,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [G: $i,H: $i] :
( ( A
= ( H @ ( G @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( H @ ( G @ ( B @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitE) ).
thf(19049,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [G: $i,H: $i] :
( ( A
= ( H @ ( G @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( H @ ( G @ ( B @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3632]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Osnd ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Ofst ) @ ( D @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Osnd ) @ ( C @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Ofst ) @ ( D @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__shift__lemma__Suc) ).
thf(6239,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Osnd ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Ofst ) @ ( D @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Osnd ) @ ( C @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Ofst ) @ ( D @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(3839,axiom,
! [A: $i] :
( ( A @ c_List_Onat__list )
<=> ( A @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) @ c_Nat__Transfer_Onat__set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__list__def) ).
thf(19889,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) @ c_Nat__Transfer_Onat__set )
=> ( A @ c_List_Onat__list ) )
& ( ( A @ c_List_Onat__list )
=> ( A @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) @ c_Nat__Transfer_Onat__set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3839]) ).
thf(2313,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I5_J) ).
thf(13718,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2313]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_Enum_On__lists ) ) )
= ( A @ ( B @ ( C @ c_Enum_On__lists ) ) @ ( A @ ( C @ c_List_Olist_OCons @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ c_COMBC ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ c_List_Omap ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_List_Oconcat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__lists_Osimps_I2_J) ).
thf(5766,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_Enum_On__lists ) ) )
= ( A @ ( B @ ( C @ c_Enum_On__lists ) ) @ ( A @ ( C @ c_List_Olist_OCons @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ c_COMBC ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ c_List_Omap ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_List_Oconcat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(5776,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(4028,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
thf(20557,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4028]) ).
thf(1240,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__mod__add3) ).
thf(9461,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(2368,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I5_J) ).
thf(13911,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2368]) ).
thf(4466,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__UNIV) ).
thf(22301,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4466]) ).
thf(4157,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
thf(21119,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4157]) ).
thf(4303,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__Diff1) ).
thf(21705,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4303]) ).
thf(1486,axiom,
! [A: $i,B: $i] :
( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ) )
& ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nat__number__of) ).
thf(10438,plain,
! [A: $i,B: $i] :
( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ) )
& ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).
thf(39054,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( c_Int_OPls @ ( c_Nat__Numeral_Oneg @ hAPP ) ) )
| ( ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= c_fTrue ) ),
inference(paramod_ordered,[status(thm)],[4775,39012]) ).
thf(39087,plain,
! [A: $i] :
( ( A != c_Int_OPls )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg )
| ( ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= c_fTrue ) ),
inference(simp,[status(thm)],[39054]) ).
thf(39094,plain,
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg )
| ( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= c_fTrue ) ),
inference(simp,[status(thm)],[39087]) ).
thf(4246,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).
thf(21492,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4246]) ).
thf(2253,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ? [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( E @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) )
<=> ? [E: $i] :
( ( A @ ( E @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).
thf(13451,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ? [E: $i] :
( ( A @ ( E @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= D )
=> ? [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( E @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ) )
& ( ? [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( E @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) )
=> ? [E: $i] :
( ( A @ ( E @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2253]) ).
thf(3137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__Suc__ivl) ).
thf(17064,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3137]) ).
thf(2706,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
thf(15354,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2706]) ).
thf(4449,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Set_Othe__elem ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__eq) ).
thf(22245,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Set_Othe__elem ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4449]) ).
thf(609,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Enum_Osublists ) @ ( B @ c_List_Oset @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__set__sublists) ).
thf(7086,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Enum_Osublists ) @ ( B @ c_List_Oset @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(4387,axiom,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(22042,plain,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4387]) ).
thf(748,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Oconcat ) @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ ( C @ tc_List_Olist @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Oconcat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__concat) ).
thf(7619,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Oconcat ) @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ ( C @ tc_List_Olist @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Oconcat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(2591,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ ( C @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__drop__subset__set__drop) ).
thf(14897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ ( C @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2591]) ).
thf(4037,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(20593,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4037]) ).
thf(2672,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_COMBK ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def) ).
thf(15232,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_COMBK ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2672]) ).
thf(746,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Wellfounded_Omeasure @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measure) ).
thf(7614,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Wellfounded_Omeasure @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(308,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).
thf(5823,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( A @ ( F @ ( B @ ( G @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) )
= ( B @ ( G @ ( A @ ( F @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
thf(6908,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( A @ ( F @ ( B @ ( G @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) )
= ( B @ ( G @ ( A @ ( F @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(2931,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_List_Olist_ONil )
= ( A @ ( B @ c_List_Oconcat ) ) )
<=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( B @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__eq__concat__conv) ).
thf(16237,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( B @ c_List_Olist_ONil ) ) )
=> ( ( B @ c_List_Olist_ONil )
= ( A @ ( B @ c_List_Oconcat ) ) ) )
& ( ( ( B @ c_List_Olist_ONil )
= ( A @ ( B @ c_List_Oconcat ) ) )
=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( B @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2931]) ).
thf(2376,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(13943,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2376]) ).
thf(456,axiom,
c_Int_OPls @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I6_J) ).
thf(6465,plain,
c_Int_OPls @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(2496,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__supI2) ).
thf(14516,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2496]) ).
thf(3328,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__inter) ).
thf(17793,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3328]) ).
thf(3570,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( B @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( B @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__le__Sup) ).
thf(18802,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( B @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( B @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3570]) ).
thf(4065,axiom,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__0) ).
thf(20698,plain,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4065]) ).
thf(1341,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oconcat ) )
= ( A @ ( C @ c_List_Oconcat ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat_Osimps_I2_J) ).
thf(9846,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oconcat ) )
= ( A @ ( C @ c_List_Oconcat ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(1959,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( F @ c_List_Olexord ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( F @ c_List_Olexord ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).
thf(12310,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( F @ c_List_Olexord ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( F @ c_List_Olexord ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( F @ c_List_Olexord ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( F @ c_List_Olexord ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1959]) ).
thf(4599,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).
thf(22797,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4599]) ).
thf(2317,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ~ ( B @ ( A @ ( A @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__irrefl) ).
thf(13731,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ~ ( B @ ( A @ ( A @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2317]) ).
thf(2413,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oidem) ).
thf(14125,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2413]) ).
thf(875,axiom,
! [A: $i] :
( ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__number) ).
thf(8090,plain,
! [A: $i] :
( ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(3437,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( A @ c_Orderings_Oord__class_Omin @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).
thf(18248,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( A @ c_Orderings_Oord__class_Omin @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3437]) ).
thf(3192,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less) ).
thf(17267,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3192]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D != C )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_Oremove1 ) ) )
= ( A @ ( D @ ( B @ c_List_Oremove1 ) ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( D = C )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_Oremove1 ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I2_J) ).
thf(8307,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D != C )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_Oremove1 ) ) )
= ( A @ ( D @ ( B @ c_List_Oremove1 ) ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( D = C )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_Oremove1 ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(3580,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
thf(18845,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3580]) ).
thf(3707,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oremove) ).
thf(19337,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3707]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).
thf(7123,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(2336,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__Suc) ).
thf(13804,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2336]) ).
thf(1687,axiom,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(11261,plain,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687]) ).
thf(1512,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Com_Ocom_Ocom__size @ ( B @ c_Com_Ocom_Ocom__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I5_J) ).
thf(10550,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Com_Ocom_Ocom__size @ ( B @ c_Com_Ocom_Ocom__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).
thf(11610,plain,
! [A: $i] : ( c_fequal @ ( A @ c_Equiv__Relations_Oequivp ) ),
inference(cnf,[status(esa)],[11609]) ).
thf(3338,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Fun_Oid @ ( B @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__id) ).
thf(17823,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Fun_Oid @ ( B @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3338]) ).
thf(2097,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ ( F @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex) ).
thf(12800,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ ( F @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2097]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( C @ c_List_Olist__all ) ) )
<=> ( A @ ( B @ ( C @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__rev) ).
thf(5603,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Olist__all ) ) )
=> ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( C @ c_List_Olist__all ) ) ) )
& ( ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( C @ c_List_Olist__all ) ) )
=> ( A @ ( B @ ( C @ c_List_Olist__all ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(2057,axiom,
! [A: $i] :
( ( A @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__UNIV) ).
thf(12671,plain,
! [A: $i] :
( ( A @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2057]) ).
thf(1360,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
=> ( ( A @ c_Orderings_Oord__class_Omax )
= ( A @ c_Orderings_Oord__class_Oless__eq @ ( A @ c_Orderings_Oord_Omax ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ord__max) ).
thf(9900,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
=> ( ( A @ c_Orderings_Oord__class_Omax )
= ( A @ c_Orderings_Oord__class_Oless__eq @ ( A @ c_Orderings_Oord_Omax ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(4021,axiom,
! [A: $i] :
( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= A ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__def) ).
thf(20529,plain,
! [A: $i] :
( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= A ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4021]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Opartition ) ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_Ofst ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter1) ).
thf(8142,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Opartition ) ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_Ofst ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(2971,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff__nat__ivl) ).
thf(16410,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2971]) ).
thf(2611,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
thf(14986,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2611]) ).
thf(2230,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
<=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__eq__1__iff) ).
thf(13340,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2230]) ).
thf(1851,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ohom__commute) ).
thf(11927,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1851]) ).
thf(3348,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Collect) ).
thf(17858,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3348]) ).
thf(1588,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).
thf(10866,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588]) ).
thf(3444,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OThe ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__eq__trivial) ).
thf(18274,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OThe ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3444]) ).
thf(1124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oremove1 ) ) )
= ( A @ ( C @ ( D @ c_List_Oremove1 ) ) @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oremove1 ) ) )
= ( A @ ( B @ ( C @ ( D @ c_List_Oremove1 ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__append) ).
thf(8980,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oremove1 ) ) )
= ( A @ ( C @ ( D @ c_List_Oremove1 ) ) @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oremove1 ) ) )
= ( A @ ( B @ ( C @ ( D @ c_List_Oremove1 ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(4192,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
thf(21270,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4192]) ).
thf(3320,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OPow @ hAPP ) )
= ( A @ ( D @ c_Set_OPow @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__INT__eq) ).
thf(17752,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OPow @ hAPP ) )
= ( A @ ( D @ c_Set_OPow @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3320]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append1) ).
thf(6224,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(579,axiom,
tc_Product__Type_Ounit @ class_Enum_Oenum,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Enum_Oenum) ).
thf(6988,plain,
tc_Product__Type_Ounit @ class_Enum_Oenum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(2106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
thf(12831,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2106]) ).
thf(1841,axiom,
! [A: $i] :
( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).
thf(11873,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1841]) ).
thf(4015,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__o) ).
thf(20510,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4015]) ).
thf(1110,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Osemiring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__double) ).
thf(8935,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Osemiring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(4707,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).
thf(23222,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4707]) ).
thf(4119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( D @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( D @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__negf) ).
thf(20964,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( D @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( D @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4119]) ).
thf(3735,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).
thf(19459,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3735]) ).
thf(2546,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Groups_Ocomm__monoid__mult )
& ( C @ class_Groups_Ocomm__monoid__add ) )
=> ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( c_Int_Onat @ ( B @ ( tc_Int_Oint @ ( C @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).
thf(14734,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Groups_Ocomm__monoid__mult )
& ( C @ class_Groups_Ocomm__monoid__add ) )
=> ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( c_Int_Onat @ ( B @ ( tc_Int_Oint @ ( C @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2546]) ).
thf(2951,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Predicate_Oreflp ) )
<=> ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflp__def) ).
thf(16328,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Relation_Orefl__on ) ) )
=> ( A @ ( B @ c_Predicate_Oreflp ) ) )
& ( ( A @ ( B @ c_Predicate_Oreflp ) )
=> ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Relation_Orefl__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2951]) ).
thf(2324,axiom,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olex ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil2__notin__lex) ).
thf(13758,plain,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olex ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2324]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(7661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(3588,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).
thf(18870,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3588]) ).
thf(639,axiom,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
thf(7193,plain,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(1121,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(8971,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(8174,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(4147,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) )
<=> ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
& ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__def) ).
thf(21074,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
& ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) ) )
& ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
& ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4147]) ).
thf(4696,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).
thf(23171,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4696]) ).
thf(24002,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4741,23986]) ).
thf(24023,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= B )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[24002]) ).
thf(24032,plain,
! [A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[24023]) ).
thf(29130,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,24032]) ).
thf(29131,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[29130]) ).
thf(29132,plain,
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[29131:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(39026,plain,
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( c_Int_OPls @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(rewrite,[status(thm)],[29132,7678]) ).
thf(4070,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I19_J) ).
thf(20730,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4070]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__add) ).
thf(5544,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(1566,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I2_J) ).
thf(10802,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566]) ).
thf(2539,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__disjoint) ).
thf(14713,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2539]) ).
thf(4698,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( E @ ( F @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Oinject) ).
thf(23182,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( E @ ( F @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4698]) ).
thf(3598,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Union) ).
thf(18905,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3598]) ).
thf(2939,axiom,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olex ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__notin__lex) ).
thf(16275,plain,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olex ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2939]) ).
thf(1149,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ ( tc_Code__Numeral_Ocode__numeral @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Osnd ) @ ( C @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_Random_Oselect__weight ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( C @ c_Product__Type_Ofst ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__member) ).
thf(9081,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ ( tc_Code__Numeral_Ocode__numeral @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Osnd ) @ ( C @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_Random_Oselect__weight ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( C @ c_Product__Type_Ofst ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(3713,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(19366,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3713]) ).
thf(3733,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( A @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int__subset) ).
thf(19447,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( A @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3733]) ).
thf(1005,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J) ).
thf(8527,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( A @ c_Divides_Odivmod__int ) @ ( B @ ( A @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__correct) ).
thf(5153,plain,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( A @ c_Divides_Odivmod__int ) @ ( B @ ( A @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1802,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ ( D @ c_Enum_Oproduct ) ) ) @ ( B @ ( D @ tc_prod ) @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__product) ).
thf(11725,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ ( D @ c_Enum_Oproduct ) ) ) @ ( B @ ( D @ tc_prod ) @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1802]) ).
thf(4095,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono2) ).
thf(20840,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4095]) ).
thf(4143,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
<=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff2) ).
thf(21055,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4143]) ).
thf(3613,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).
thf(18958,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3613]) ).
thf(1523,axiom,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__mod__nat__number__of) ).
thf(10597,plain,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).
thf(3998,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__inverse) ).
thf(20451,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3998]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__map) ).
thf(8839,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(2147,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) )
=> ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ball__nth) ).
thf(13014,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) )
=> ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2147]) ).
thf(2619,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( A @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( A @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).
thf(15042,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( A @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( A @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2619]) ).
thf(573,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).
thf(6963,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(1668,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(11197,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).
thf(1642,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ ( C @ ( E @ ( D @ ( E @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__scomp) ).
thf(11084,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ ( C @ ( E @ ( D @ ( E @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642]) ).
thf(3503,axiom,
tc_Com_Ocom @ class_Nat_Osize,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com__Ocom__Nat_Osize) ).
thf(18508,plain,
tc_Com_Ocom @ class_Nat_Osize,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3503]) ).
thf(4204,axiom,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1) ).
thf(21317,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4204]) ).
thf(2198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimage__iff) ).
thf(13232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2198]) ).
thf(1952,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
<=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
thf(12282,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1952]) ).
thf(1838,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).
thf(11856,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1838]) ).
thf(33161,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Nat__Numeral_Oneg @ hAPP ) ) )
| ~ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[4775,13558]) ).
thf(33554,plain,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg )
| ~ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[33161]) ).
thf(33781,plain,
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg )
| ~ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[33554]) ).
thf(43894,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg )
| ~ ( A @ c_Groups_Oone__class_Oone @ hBOOL )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4735,33781]) ).
thf(43895,plain,
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg )
| ~ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hBOOL )
| ~ ( tc_Int_Oint @ class_Rings_Oring__1 ) ),
inference(pattern_uni,[status(thm)],[43894:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(43945,plain,
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg )
| ~ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hBOOL )
| ~ $true ),
inference(rewrite,[status(thm)],[43895,5382]) ).
thf(43946,plain,
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg )
| ~ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hBOOL ) ),
inference(simp,[status(thm)],[43945]) ).
thf(43947,plain,
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8089,43946]) ).
thf(43948,plain,
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg ) ),
inference(simp,[status(thm)],[43947]) ).
thf(43963,plain,
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= c_fTrue )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg ) ),
inference(simp,[status(thm)],[43948]) ).
thf(3705,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).
thf(19332,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3705]) ).
thf(3572,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(18813,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3572]) ).
thf(2717,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(15395,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2717]) ).
thf(4537,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D2) ).
thf(22565,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4537]) ).
thf(2769,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__nat) ).
thf(15592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2769]) ).
thf(2999,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).
thf(16548,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2999]) ).
thf(2001,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatLeast ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
thf(12469,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OatLeast ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatLeast ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2001]) ).
thf(2075,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(12736,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2075]) ).
thf(1325,axiom,
( c_FunDef_Omax__strict
= ( c_FunDef_Opair__less @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Omax__ext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__strict__def) ).
thf(9782,plain,
( c_FunDef_Omax__strict
= ( c_FunDef_Opair__less @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Omax__ext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(3334,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).
thf(17812,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3334]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__add) ).
thf(4765,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3931,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageD) ).
thf(20241,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3931]) ).
thf(1747,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).
thf(11524,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747]) ).
thf(2975,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( B @ ( A @ c_List_Oset @ hAPP ) @ ( B @ ( A @ c_List_Ohd @ hAPP ) @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__in__set) ).
thf(16432,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( B @ ( A @ c_List_Oset @ hAPP ) @ ( B @ ( A @ c_List_Ohd @ hAPP ) @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2975]) ).
thf(1140,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__neg__1__number__of) ).
thf(9044,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(2151,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
thf(13026,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2151]) ).
thf(1818,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Osym ) )
=> ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__rtrancl) ).
thf(11787,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Osym ) )
=> ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1818]) ).
thf(2926,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__geq) ).
thf(16220,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2926]) ).
thf(3922,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lessThan) ).
thf(20212,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3922]) ).
thf(3033,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).
thf(16666,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3033]) ).
thf(975,axiom,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistsp ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp_Oequations_I1_J) ).
thf(8422,plain,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistsp ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(2349,axiom,
! [A: $i] :
( ( A @ c_Nat__Transfer_Ois__nat )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__nat__def) ).
thf(13844,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Nat__Transfer_Ois__nat ) )
& ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2349]) ).
thf(1105,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).
thf(8923,plain,
tc_Code__Numeral_Ocode__numeral @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(765,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Nil) ).
thf(7687,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(3892,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Obounded__lattice__top )
=> ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ c_Orderings_Otop__class_Otop ) )
<=> ( ( A
= ( C @ c_Orderings_Otop__class_Otop ) )
& ( B
= ( C @ c_Orderings_Otop__class_Otop ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__eq__top__iff) ).
thf(20096,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Obounded__lattice__top )
=> ( ( ( ( A
= ( C @ c_Orderings_Otop__class_Otop ) )
& ( B
= ( C @ c_Orderings_Otop__class_Otop ) ) )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ c_Orderings_Otop__class_Otop ) ) )
& ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ c_Orderings_Otop__class_Otop ) )
=> ( ( A
= ( C @ c_Orderings_Otop__class_Otop ) )
& ( B
= ( C @ c_Orderings_Otop__class_Otop ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3892]) ).
thf(4609,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff__insert) ).
thf(22835,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4609]) ).
thf(3999,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__conj) ).
thf(20454,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3999]) ).
thf(1401,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__imp__rtrancl) ).
thf(10069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).
thf(863,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__self) ).
thf(8049,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(1856,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__bot )
=> ( ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__left) ).
thf(11940,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__bot )
=> ( ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1856]) ).
thf(3324,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
thf(17767,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3324]) ).
thf(2697,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( tc_HOL_Obool @ ( D @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__bex) ).
thf(15307,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( tc_HOL_Obool @ ( D @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( tc_HOL_Obool @ ( D @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2697]) ).
thf(2811,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinsert__remove) ).
thf(15747,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2811]) ).
thf(3587,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__le__eq__Un0) ).
thf(18867,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3587]) ).
thf(969,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zdiv__mult__2) ).
thf(8393,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( C @ c_List_Olist_ONil ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( D @ ( C @ c_List_Ohd @ hAPP ) @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__map) ).
thf(6260,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( C @ c_List_Olist_ONil ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( D @ ( C @ c_List_Ohd @ hAPP ) @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(1994,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_Relation_Orefl__on ) ) ) )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__UNION) ).
thf(12442,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_Relation_Orefl__on ) ) ) )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1994]) ).
thf(3887,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__insert) ).
thf(20075,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3887]) ).
thf(2005,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).
thf(12486,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2005]) ).
thf(1313,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).
thf(9750,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(2187,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(13196,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2187]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Orotate ) @ hAPP ) @ ( C @ ( D @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_List_Orotate ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__rotate) ).
thf(6378,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Orotate ) @ hAPP ) @ ( C @ ( D @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_List_Orotate ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(2027,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Osublist ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__sublistD) ).
thf(12553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Osublist ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2027]) ).
thf(1115,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_List_Olistrel ) )
= ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
thf(8955,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_List_Olistrel ) )
= ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(2129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN) ).
thf(12938,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2129]) ).
thf(4544,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(22590,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4544]) ).
thf(1965,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Fun_Oid @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id) ).
thf(12346,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Fun_Oid @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1965]) ).
thf(4523,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Set_OPow @ hAPP ) )
= ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__insert) ).
thf(22514,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Set_OPow @ hAPP ) )
= ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4523]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult) ).
thf(6891,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(927,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__code__numeral__code) ).
thf(8262,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(2997,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__eqI) ).
thf(16537,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2997]) ).
thf(3539,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
<=> ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).
thf(18641,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3539]) ).
thf(3395,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
thf(18059,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3395]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power__minus) ).
thf(8609,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(819,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= C )
=> ( ( B
= ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).
thf(7863,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= C )
=> ( ( B
= ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(2538,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ~ ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
| ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).
thf(14702,plain,
! [A: $i,B: $i] :
( ( ( ~ ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
| ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ~ ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
| ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2538]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).
thf(5417,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(3054,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__distrib) ).
thf(16754,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3054]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__update) ).
thf(7656,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(837,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ c_Product__Type_OPair ) @ ( A @ ( B @ ( C @ tc_prod ) @ ( B @ ( C @ ( D @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__Pair) ).
thf(7941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ c_Product__Type_OPair ) @ ( A @ ( B @ ( C @ tc_prod ) @ ( B @ ( C @ ( D @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(39757,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( c_Int_OPls @ ( c_Nat__Numeral_Oneg @ hAPP ) ) )
| ~ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[4775,39032]) ).
thf(39807,plain,
! [A: $i] :
( ( A != c_Int_OPls )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg )
| ~ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[39757]) ).
thf(39818,plain,
( ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= c_Nat__Numeral_Oneg )
| ~ ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[39807]) ).
thf(3060,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(16769,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3060]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OdropWhile ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OdropWhile ) ) )
= ( A @ ( D @ ( B @ c_List_OdropWhile ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).
thf(5887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OdropWhile ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OdropWhile ) ) )
= ( A @ ( D @ ( B @ c_List_OdropWhile ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(2259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(13480,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2259]) ).
thf(3897,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__anti__mono) ).
thf(20120,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3897]) ).
thf(3864,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
thf(20004,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3864]) ).
thf(223,axiom,
! [A: $i] :
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Code__Numeral_OSuc__code__numeral ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).
thf(5513,plain,
! [A: $i] :
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Code__Numeral_OSuc__code__numeral ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1085,axiom,
! [A: $i] :
( ( A @ c_Divides_Oadjust )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBB ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBS ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_adjust__def) ).
thf(8824,plain,
! [A: $i] :
( ( A @ c_Divides_Oadjust )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBB ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBS ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(4475,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__right) ).
thf(22332,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4475]) ).
thf(4613,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__UNIV) ).
thf(22856,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4613]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(5909,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(4378,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OField @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__empty) ).
thf(22008,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OField @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4378]) ).
thf(2301,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
thf(13667,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2301]) ).
thf(848,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__diff) ).
thf(7972,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(1412,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
thf(10111,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(167,axiom,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( A @ c_Int_Oring__1__class_OInts @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__1) ).
thf(5295,plain,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( A @ c_Int_Oring__1__class_OInts @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(3700,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Omax__extp ) ) ) )
<=> ( C @ ( D @ c_Wellfounded_Omax__ext ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).
thf(19315,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Wellfounded_Omax__ext ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Omax__extp ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Omax__extp ) ) ) )
=> ( C @ ( D @ c_Wellfounded_Omax__ext ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3700]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ c_Divides_OnegDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__pos) ).
thf(5249,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ c_Divides_OnegDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(4043,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
thf(20614,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4043]) ).
thf(3491,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_List_Oupt ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__rec__number__of) ).
thf(18462,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_List_Oupt ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3491]) ).
thf(3174,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
thf(17222,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3174]) ).
thf(3232,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( D @ ( B @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
thf(17426,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( D @ ( B @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3232]) ).
thf(1560,axiom,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
thf(10783,plain,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560]) ).
thf(2744,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__type) ).
thf(15506,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2744]) ).
thf(4702,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
thf(23203,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4702]) ).
thf(3597,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).
thf(18902,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3597]) ).
thf(1037,axiom,
! [A: $i] :
( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__return__embed) ).
thf(8626,plain,
! [A: $i] :
( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1723,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olist_ONil @ ( B @ ( C @ ( D @ c_List_Ofoldr ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr_Osimps_I1_J) ).
thf(11414,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olist_ONil @ ( B @ ( C @ ( D @ c_List_Ofoldr ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723]) ).
thf(1378,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__beta) ).
thf(9985,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(3745,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Odistrib__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup2__distrib) ).
thf(19511,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Odistrib__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3745]) ).
thf(3254,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [C: $i] :
! [D: $i] :
( ( A @ ( D @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__maxlen) ).
thf(17514,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [C: $i] :
! [D: $i] :
( ( A @ ( D @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3254]) ).
thf(2576,axiom,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zle) ).
thf(14848,plain,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2576]) ).
thf(3561,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__set) ).
thf(18770,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3561]) ).
thf(1900,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__distrib2) ).
thf(12104,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1900]) ).
thf(726,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).
thf(7527,plain,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(1192,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onat__gcd__rel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onat__gcd__rel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ( E
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( E @ ( D @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Opinduct) ).
thf(9256,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onat__gcd__rel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Nitpick_Onat__gcd__rel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ( E
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( E @ ( D @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(3604,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).
thf(18924,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3604]) ).
thf(4536,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int2) ).
thf(22562,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4536]) ).
thf(4171,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__eq__positive) ).
thf(21170,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4171]) ).
thf(2059,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).
thf(12677,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2059]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ c_List_Olist_ONil @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( E @ c_List_Olist_ONil @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append1__eq__conv) ).
thf(7646,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( E @ c_List_Olist_ONil @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( E @ c_List_Olist_ONil @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( E @ c_List_Olist_ONil @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( E @ c_List_Olist_ONil @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(4486,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold__graphE) ).
thf(22371,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4486]) ).
thf(2308,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
thf(13703,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2308]) ).
thf(2046,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ class_Groups_Ocomm__monoid__add )
=> ( ( D @ ( E @ ( F @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( C
= ( D @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( ! [I: $i] :
( ( D @ ( I @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( B @ hAPP ) )
= ( I @ ( E @ hAPP ) @ ( A @ hAPP ) ) ) )
=> ( ( C @ ( A @ ( H @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( H @ ( G @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__cong) ).
thf(12628,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ class_Groups_Ocomm__monoid__add )
=> ( ( D @ ( E @ ( F @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( C
= ( D @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( ! [I: $i] :
( ( D @ ( I @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( B @ hAPP ) )
= ( I @ ( E @ hAPP ) @ ( A @ hAPP ) ) ) )
=> ( ( C @ ( A @ ( H @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( H @ ( G @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2046]) ).
thf(2822,axiom,
tc_HOL_Obool @ class_Complete__Lattice_Ocomplete__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
thf(15815,plain,
tc_HOL_Obool @ class_Complete__Lattice_Ocomplete__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2822]) ).
thf(2247,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
thf(13419,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2247]) ).
thf(2134,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).
thf(12953,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2134]) ).
thf(4624,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__singleton) ).
thf(22888,plain,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4624]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Orotate ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__length01) ).
thf(8215,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Orotate ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(4096,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(20844,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4096]) ).
thf(3582,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
thf(18853,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3582]) ).
thf(2936,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ounion__disjoint) ).
thf(16265,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2936]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ~ ( A @ ( D @ c_List_Oset @ hAPP ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__insort) ).
thf(8333,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ~ ( A @ ( D @ c_List_Oset @ hAPP ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ~ ( A @ ( D @ c_List_Oset @ hAPP ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(2431,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
thf(14231,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2431]) ).
thf(1188,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i,E: $i] :
( ( ( A
= ( E @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__neg__lemma) ).
thf(9237,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ! [D: $i,E: $i] :
( ( ( A
= ( E @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( A
= ( E @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(35127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( C @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) )
| ( ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4741,33754]) ).
thf(35128,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Int_Oint @ class_Rings_Oring__1 ) ),
inference(pattern_uni,[status(thm)],[35127:[bind(A,$thf( tc_Int_Oint )),bind(B,$thf( B )),bind(C,$thf( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ))]]) ).
thf(35277,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Int_Oint @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[35128]) ).
thf(35687,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[35277,5382]) ).
thf(35688,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[35687]) ).
thf(39009,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(rewrite,[status(thm)],[35688,7678]) ).
thf(4533,axiom,
tc_HOL_Obool @ class_Lattices_Obounded__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
thf(22555,plain,
tc_HOL_Obool @ class_Lattices_Obounded__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4533]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oapsnd ) ) ) )
= ( A @ ( B @ c_Fun_Oid @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_Omap__pair ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__def) ).
thf(4919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oapsnd ) ) ) )
= ( A @ ( B @ c_Fun_Oid @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_Omap__pair ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(4376,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_OPow @ hAPP ) )
!= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__not__empty) ).
thf(22001,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_OPow @ hAPP ) )
!= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4376]) ).
thf(3021,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Obutlast ) @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__butlastD) ).
thf(16615,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Obutlast ) @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3021]) ).
thf(1579,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__neg) ).
thf(10840,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ~ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__list__update) ).
thf(5996,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ~ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( A @ ( E @ ( B @ ( F @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( F @ ( A @ ( E @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__swap) ).
thf(5722,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( A @ ( E @ ( B @ ( F @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( F @ ( A @ ( E @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1793,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).
thf(11692,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1793]) ).
thf(1808,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Com_Ocom_Ocom__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I6_J) ).
thf(11747,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Com_Ocom_Ocom__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1808]) ).
thf(1663,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( A @ ( C @ c_Wellfounded_Omlex__prod ) ) @ ( C @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__mlex) ).
thf(11179,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( A @ ( C @ c_Wellfounded_Omlex__prod ) ) @ ( C @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).
thf(1099,axiom,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistrelp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
thf(8903,plain,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistrelp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(3662,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(19154,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3662]) ).
thf(3882,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__D2) ).
thf(20060,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3882]) ).
thf(1919,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( A @ ( A @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).
thf(12168,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( A @ ( A @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1919]) ).
thf(3195,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( A @ ( C @ c_Wellfounded_Owf ) )
=> ( ( ( A @ ( C @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( C @ ( C @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Un) ).
thf(17282,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( A @ ( C @ c_Wellfounded_Owf ) )
=> ( ( ( A @ ( C @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( C @ ( C @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3195]) ).
thf(3157,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__Int__eq) ).
thf(17150,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3157]) ).
thf(4323,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I2_J) ).
thf(21800,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4323]) ).
thf(3026,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__1) ).
thf(16637,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3026]) ).
thf(2896,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supE) ).
thf(16100,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2896]) ).
thf(1319,axiom,
( ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ c_Finite__Set_Ocard @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__bool) ).
thf(9765,plain,
( ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ c_Finite__Set_Ocard @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(736,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__dropWhile__le) ).
thf(7582,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(2227,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I7_J) ).
thf(13331,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2227]) ).
thf(4493,axiom,
tc_HOL_Obool @ class_Lattices_Obounded__lattice__top,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
thf(22396,plain,
tc_HOL_Obool @ class_Lattices_Obounded__lattice__top,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4493]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__drop) ).
thf(9231,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(3920,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Domain) ).
thf(20207,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3920]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OposDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OposDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Opinduct) ).
thf(5808,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OposDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OposDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(2777,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= B )
=> ( ( A @ ( C @ hAPP ) @ ( D @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(15614,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= B )
=> ( ( A @ ( C @ hAPP ) @ ( D @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2777]) ).
thf(115,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Osucc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I2_J) ).
thf(5138,plain,
! [A: $i] :
( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Osucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I2_J) ).
thf(6615,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(4428,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Obot )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
thf(22173,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Obot )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4428]) ).
thf(2142,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ) )
& ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton__if) ).
thf(12982,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ) )
& ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2142]) ).
thf(3826,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Un) ).
thf(19815,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3826]) ).
thf(1250,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing) ).
thf(9502,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(3699,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Otrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq) ).
thf(19309,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Otrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Otrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3699]) ).
thf(1937,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I10_J) ).
thf(12233,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1937]) ).
thf(1435,axiom,
! [A: $i] :
( ( A @ c_COMBI @ ( A @ ( A @ c_List_Omap ) @ hAPP ) )
= ( A @ tc_List_Olist @ c_Fun_Oid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oidentity) ).
thf(10202,plain,
! [A: $i] :
( ( A @ c_COMBI @ ( A @ ( A @ c_List_Omap ) @ hAPP ) )
= ( A @ tc_List_Olist @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(2799,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( A @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__Int__subset) ).
thf(15707,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( A @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2799]) ).
thf(343,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
thf(5969,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(3803,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_OwfP ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__wfPD) ).
thf(19740,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_OwfP ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3803]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ c_Lazy__Sequence_Oanamorph ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( E @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Lazy__Sequence_Oanamorph ) ) @ hAPP ) @ ( C @ c_List_Olist_OCons @ ( D @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ ( C @ tc_List_Olist @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ ( C @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ ( C @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ c_COMBB ) ) @ ( C @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ tc_fun ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( A @ ( C @ c_List_Olist_ONil @ ( D @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ c_Option_Ooption_Ooption__case ) ) ) ) ) ) )
& ( ( E
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ c_Lazy__Sequence_Oanamorph ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_List_Olist_ONil @ ( D @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_anamorph_Osimps) ).
thf(6561,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ c_Lazy__Sequence_Oanamorph ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( E @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Lazy__Sequence_Oanamorph ) ) @ hAPP ) @ ( C @ c_List_Olist_OCons @ ( D @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ ( C @ tc_List_Olist @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ ( C @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ ( C @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ c_COMBB ) ) @ ( C @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ tc_fun ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ ( D @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( A @ ( C @ c_List_Olist_ONil @ ( D @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ tc_List_Olist @ tc_prod ) @ c_Option_Ooption_Ooption__case ) ) ) ) ) ) )
& ( ( E
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ c_Lazy__Sequence_Oanamorph ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_List_Olist_ONil @ ( D @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(3763,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__iff) ).
thf(19583,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3763]) ).
thf(2283,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( B @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= B )
=> ( ( ( B @ ( C @ ( C @ c_Relation_ODomain ) @ hAPP ) )
= A )
=> ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__equivI) ).
thf(13584,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( B @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= B )
=> ( ( ( B @ ( C @ ( C @ c_Relation_ODomain ) @ hAPP ) )
= A )
=> ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2283]) ).
thf(1390,axiom,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus1__eq__if) ).
thf(10030,plain,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).
thf(4009,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__Int) ).
thf(20490,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4009]) ).
thf(3342,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__min__eq__max) ).
thf(17834,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3342]) ).
thf(2365,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__psubset__iff) ).
thf(13896,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oorder )
=> ( ( ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2365]) ).
thf(3204,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ~ ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( D @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).
thf(17321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ~ ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( D @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3204]) ).
thf(374,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).
thf(6084,plain,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(2367,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(13907,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2367]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( F @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
<=> ( A @ ( D @ ( B @ ( E @ ( C @ ( tc_HOL_Obool @ ( F @ c_COMBB ) ) @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__map2) ).
thf(5230,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( D @ ( B @ ( E @ ( C @ ( tc_HOL_Obool @ ( F @ c_COMBB ) ) @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Olist__all2 ) ) ) ) )
=> ( A @ ( B @ ( F @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) ) )
& ( ( A @ ( B @ ( F @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
=> ( A @ ( D @ ( B @ ( E @ ( C @ ( tc_HOL_Obool @ ( F @ c_COMBB ) ) @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Olist__all2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(3848,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(19941,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3848]) ).
thf(3446,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil1) ).
thf(18280,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3446]) ).
thf(772,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod__number__of) ).
thf(7706,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(4162,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( A @ ( C @ ( B @ ( D @ ( D @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).
thf(21142,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( A @ ( C @ ( B @ ( D @ ( D @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4162]) ).
thf(4271,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__eq) ).
thf(21583,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4271]) ).
thf(1905,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B
!= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__subset) ).
thf(12119,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B
!= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1905]) ).
thf(2201,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ ( E @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__subset) ).
thf(13245,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ ( E @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2201]) ).
thf(1405,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( B @ ( C @ c_List_Oremove1 ) ) @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__remove1) ).
thf(10079,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( B @ ( C @ c_List_Oremove1 ) ) @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__int) ).
thf(6578,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(530,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__2__cases) ).
thf(6792,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(786,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
<=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__equals__nth__mono) ).
thf(7753,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ c_List_Olinorder__class_Osorted ) ) )
& ( ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(2501,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(14534,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2501]) ).
thf(2966,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( B @ ( D @ ( F @ ( E @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ImageE) ).
thf(16390,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( B @ ( D @ ( F @ ( E @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2966]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBK ) @ ( B @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_ONil @ ( B @ ( B @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Oconcat ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( B @ c_List_Ohd @ ( B @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__filter__head) ).
thf(5960,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBK ) @ ( B @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_ONil @ ( B @ ( B @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Oconcat ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( B @ c_List_Ohd @ ( B @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(3345,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Osubset__idem) ).
thf(17851,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3345]) ).
thf(1726,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( A @ ( c_Int_Onat @ ( c_fequal @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__Suc) ).
thf(11427,plain,
! [A: $i,B: $i] :
( ( ( A @ ( c_Int_Onat @ ( c_fequal @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( A @ ( c_Int_Onat @ ( c_fequal @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726]) ).
thf(2447,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBI @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__def) ).
thf(14303,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBI @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2447]) ).
thf(2355,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ ( F @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__image__INT) ).
thf(13864,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ ( F @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2355]) ).
thf(2670,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Nitpick_Oprod ) ) ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oprod__def) ).
thf(15226,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Nitpick_Oprod ) ) ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2670]) ).
thf(3916,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnCI) ).
thf(20192,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3916]) ).
thf(1618,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) )
=> ( ( C @ ( D @ c_List_Otranspose ) @ ( D @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( D @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( D @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ c_List_Otranspose ) @ ( D @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__nth__transpose__sorted) ).
thf(10993,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) )
=> ( ( C @ ( D @ c_List_Otranspose ) @ ( D @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( D @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( D @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ c_List_Otranspose ) @ ( D @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618]) ).
thf(4365,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__binary) ).
thf(21957,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4365]) ).
thf(3264,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ c_List_Olists ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__mono) ).
thf(17542,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ c_List_Olists ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3264]) ).
thf(3688,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__inf__iff) ).
thf(19268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3688]) ).
thf(1025,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__divide__distrib) ).
thf(8591,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
<=> ( ( ( A
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
& ( B
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
| ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__eq__1__iff) ).
thf(6001,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
& ( B
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
| ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( ( A
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
& ( B
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
| ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(4721,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
thf(23271,plain,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4721]) ).
thf(4672,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= A ) )
& ( ( D
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__constant) ).
thf(23068,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= A ) )
& ( ( D
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4672]) ).
thf(740,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Oremove1 ) ) )
= ( B @ ( A @ ( C @ c_List_OremoveAll ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remove1__removeAll) ).
thf(7599,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Oremove1 ) ) )
= ( B @ ( A @ ( C @ c_List_OremoveAll ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(3520,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( D @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
thf(18572,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( D @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3520]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).
thf(6469,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(1733,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
thf(11464,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ) )
& ( ( ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733]) ).
thf(4442,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(22218,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4442]) ).
thf(2736,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0) ).
thf(15474,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2736]) ).
thf(1165,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).
thf(9154,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(2787,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).
thf(15660,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2787]) ).
thf(4066,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).
thf(20701,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4066]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__app__Cons__same) ).
thf(7920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(2702,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(15334,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2702]) ).
thf(3406,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I13_J) ).
thf(18095,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3406]) ).
thf(1059,axiom,
c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ c_Relation_Otrans ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__than) ).
thf(8718,plain,
c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ c_Relation_Otrans ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(4328,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).
thf(21819,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4328]) ).
thf(3522,axiom,
tc_HOL_Obool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(18577,plain,
tc_HOL_Obool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3522]) ).
thf(4086,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).
thf(20808,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4086]) ).
thf(3435,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le1) ).
thf(18244,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3435]) ).
thf(4309,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_If @ ( F @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( D @ ( c_fNot @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Set_OCollect @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( F @ c_Set_OCollect @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_if__image__distrib) ).
thf(21724,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_If @ ( F @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( D @ ( c_fNot @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Set_OCollect @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( F @ c_Set_OCollect @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4309]) ).
thf(4247,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Relation_Oantisym ) )
=> ( B @ ( C @ c_Relation_Oantisym ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__subset) ).
thf(21495,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Relation_Oantisym ) )
=> ( B @ ( C @ c_Relation_Oantisym ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4247]) ).
thf(2910,axiom,
tc_Nat_Onat @ class_Nat_Osize,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osize) ).
thf(16152,plain,
tc_Nat_Onat @ class_Nat_Osize,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2910]) ).
thf(1236,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(9451,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(3976,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnI) ).
thf(20384,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3976]) ).
thf(2877,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(16012,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2877]) ).
thf(2556,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Osym ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_symD) ).
thf(14776,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Osym ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2556]) ).
thf(3658,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_fdisj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) )
= ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__disj__eq) ).
thf(19134,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_fdisj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) )
= ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3658]) ).
thf(4179,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i,E: $i] :
( A
= ( E @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__decomp) ).
thf(21211,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i,E: $i] :
( A
= ( E @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i,E: $i] :
( A
= ( E @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4179]) ).
thf(1142,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( C @ ( B @ c_List_Ohd @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__append2) ).
thf(9049,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( C @ ( B @ c_List_Ohd @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(3625,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
<=> ! [C: $i] :
( ? [D: $i] : ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
thf(19017,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ? [D: $i] : ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) )
& ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ! [C: $i] :
( ? [D: $i] : ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3625]) ).
thf(3235,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(17436,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3235]) ).
thf(4723,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Nitpick_Ofold__graph_H ) ) ) ) ) )
<=> ( ? [H: $i,I: $i] :
( ( I @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( H @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Nitpick_Ofold__graph_H ) ) ) ) ) )
& ( C @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( A @ ( B @ ( E @ hAPP ) @ hAPP ) )
= ( I @ ( H @ ( E @ hAPP ) @ hAPP ) ) ) )
| ( ( ( A @ ( B @ ( E @ hAPP ) @ hAPP ) )
= D )
& ( C
= ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
thf(23276,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ? [H: $i,I: $i] :
( ( I @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( H @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Nitpick_Ofold__graph_H ) ) ) ) ) )
& ( C @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( A @ ( B @ ( E @ hAPP ) @ hAPP ) )
= ( I @ ( H @ ( E @ hAPP ) @ hAPP ) ) ) )
| ( ( ( A @ ( B @ ( E @ hAPP ) @ hAPP ) )
= D )
& ( C
= ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) )
=> ( A @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ) )
& ( ( A @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Nitpick_Ofold__graph_H ) ) ) ) ) )
=> ( ? [H: $i,I: $i] :
( ( I @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( H @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Nitpick_Ofold__graph_H ) ) ) ) ) )
& ( C @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( A @ ( B @ ( E @ hAPP ) @ hAPP ) )
= ( I @ ( H @ ( E @ hAPP ) @ hAPP ) ) ) )
| ( ( ( A @ ( B @ ( E @ hAPP ) @ hAPP ) )
= D )
& ( C
= ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4723]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_List_Oupto ) @ ( C @ ( tc_Int_Oint @ c_List_Olist__ex ) ) )
<=> ~ ( A @ ( B @ ( C @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ c_List_Oall__interval__int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__iff__not__all__inverval__int) ).
thf(6422,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( A @ ( B @ ( C @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ c_List_Oall__interval__int ) ) )
=> ( A @ ( B @ c_List_Oupto ) @ ( C @ ( tc_Int_Oint @ c_List_Olist__ex ) ) ) )
& ( ( A @ ( B @ c_List_Oupto ) @ ( C @ ( tc_Int_Oint @ c_List_Olist__ex ) ) )
=> ~ ( A @ ( B @ ( C @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ c_List_Oall__interval__int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(4464,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [E: $i,F: $i] : ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oclosed) ).
thf(22296,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [E: $i,F: $i] : ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4464]) ).
thf(3915,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) @ hBOOL )
=> ( ! [E: $i,F: $i] :
( ( F @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( F @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) @ hBOOL )
=> ( F @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset__induct) ).
thf(20185,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) @ hBOOL )
=> ( ! [E: $i,F: $i] :
( ( F @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( F @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) @ hBOOL )
=> ( F @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3915]) ).
thf(1283,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__functions) ).
thf(9652,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(3103,axiom,
( ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeast @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__atLeast__UNIV) ).
thf(16941,plain,
( ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeast @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3103]) ).
thf(1595,axiom,
! [A: $i] :
( ( A @ class_Groups_Osgn__if )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Osgn__class_Osgn ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn0) ).
thf(10890,plain,
! [A: $i] :
( ( A @ class_Groups_Osgn__if )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Osgn__class_Osgn ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).
thf(194,axiom,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
thf(5400,plain,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(3020,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_Relation_ORange ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__converse) ).
thf(16612,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_Relation_ORange ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3020]) ).
thf(4364,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Un__distrib) ).
thf(21954,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4364]) ).
thf(2280,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__less__nat) ).
thf(13559,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2280]) ).
thf(4228,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(21400,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4228]) ).
thf(3866,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(20009,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3866]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__mult) ).
thf(4943,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(3207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD) ).
thf(17336,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3207]) ).
thf(4239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(21465,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4239]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Product__Type_Osnd ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__conv) ).
thf(7860,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Product__Type_Osnd ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(1274,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
thf(9617,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(4450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= ( C @ c_Fun_Oid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oempty) ).
thf(22248,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= ( C @ c_Fun_Oid ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4450]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Orev @ hAPP ) @ ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_OtakeWhile ) ) )
= ( B @ ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Otl @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__neq__rev) ).
thf(7709,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Orev @ hAPP ) @ ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_OtakeWhile ) ) )
= ( B @ ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Otl @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(630,axiom,
! [A: $i] :
( ( A @ class_Enum_Oenum )
=> ( A @ tc_Option_Ooption @ class_Enum_Oenum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Enum_Oenum) ).
thf(7162,plain,
! [A: $i] :
( ( A @ class_Enum_Oenum )
=> ( A @ tc_Option_Ooption @ class_Enum_Oenum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(1027,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( A @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__drop) ).
thf(8597,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( A @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(4630,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__eq__Union) ).
thf(22913,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4630]) ).
thf(1519,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
thf(10582,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519]) ).
thf(1422,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Rings_Osemiring__0 )
=> ( ( A @ ( B @ ( G @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( G @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( G @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ ( E @ ( G @ c_Groups_Otimes__class_Otimes @ ( F @ ( G @ ( G @ tc_fun ) @ ( G @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ ( G @ c_COMBB ) ) @ ( F @ ( G @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ tc_fun ) @ ( G @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( G @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( F @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( G @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__product) ).
thf(10155,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Rings_Osemiring__0 )
=> ( ( A @ ( B @ ( G @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( G @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( G @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ ( E @ ( G @ c_Groups_Otimes__class_Otimes @ ( F @ ( G @ ( G @ tc_fun ) @ ( G @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ ( G @ c_COMBB ) ) @ ( F @ ( G @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ tc_fun ) @ ( G @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( G @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( F @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( G @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(4587,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).
thf(22753,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4587]) ).
thf(3343,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I7_J) ).
thf(17837,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3343]) ).
thf(3697,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ ( C @ ( C @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
thf(19301,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ ( C @ ( C @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ ( C @ ( C @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3697]) ).
thf(4146,axiom,
! [A: $i] :
( ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) )
<=> ! [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).
thf(21067,plain,
! [A: $i] :
( ( ! [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
=> ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) )
=> ! [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4146]) ).
thf(666,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( B @ c_Relation_OId__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Id__on) ).
thf(7287,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( B @ c_Relation_OId__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olex ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
& ( A @ ( D @ c_List_Olexord ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__lex) ).
thf(7590,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
& ( A @ ( D @ c_List_Olexord ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ c_List_Olex ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_List_Olex ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
& ( A @ ( D @ c_List_Olexord ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(846,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(7968,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(836,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(7938,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(1432,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).
thf(10194,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(2004,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__timesf) ).
thf(12483,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2004]) ).
thf(1330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i,F: $i] :
( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
thf(9798,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i,F: $i] :
( ( ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(2636,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__trans) ).
thf(15100,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2636]) ).
thf(4156,axiom,
! [A: $i,B: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_List_Olexn ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn_Osimps_I1_J) ).
thf(21116,plain,
! [A: $i,B: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_List_Olexn ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4156]) ).
thf(2902,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) )
<=> ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).
thf(16122,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) )
=> ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2902]) ).
thf(4418,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
thf(22138,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4418]) ).
thf(3178,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__maxI2) ).
thf(17231,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3178]) ).
thf(3686,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Oantisym ) )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__def) ).
thf(19249,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = D ) ) )
=> ( A @ ( B @ c_Relation_Oantisym ) ) )
& ( ( A @ ( B @ c_Relation_Oantisym ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3686]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(9010,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(463,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
thf(6490,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(6491,plain,
~ ? [A: $i] :
( ( A @ c_Int_OBit1 )
= c_Int_OPls ),
inference(miniscope,[status(thm)],[6490]) ).
thf(6492,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
inference(cnf,[status(esa)],[6491]) ).
thf(6493,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
inference(lifteq,[status(thm)],[6492]) ).
thf(1647,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__abs__mult__distrib) ).
thf(11105,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647]) ).
thf(750,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__2) ).
thf(7639,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( D @ ( C @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Product__Type_Ofst ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__apsnd) ).
thf(5474,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( D @ ( C @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Product__Type_Ofst ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(4329,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).
thf(21822,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4329]) ).
thf(2474,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Odistrib__lattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib1) ).
thf(14434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Odistrib__lattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2474]) ).
thf(1511,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Odivmod__nat ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__div__mod) ).
thf(10547,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Odivmod__nat ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511]) ).
thf(4394,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
thf(22064,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4394]) ).
thf(4437,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( A @ ( C @ ( B @ ( D @ c_FunDef_Orp__inv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_FunDef_Oreduction__pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(22199,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( A @ ( C @ ( B @ ( D @ c_FunDef_Orp__inv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_FunDef_Oreduction__pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4437]) ).
thf(2108,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(12835,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2108]) ).
thf(2613,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
thf(14994,plain,
! [A: $i,B: $i] :
( ( ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2613]) ).
thf(1098,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( ( B @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ tc_prod ) @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append) ).
thf(8900,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( ( B @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ tc_prod ) @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(3331,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( E @ c_List_Ozip ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ tc_List_Olist @ ( E @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Olist_OCons @ ( E @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ c_COMBB ) ) @ ( E @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Olist_ONil @ ( E @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons) ).
thf(17800,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( E @ c_List_Ozip ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ tc_List_Olist @ ( E @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Olist_OCons @ ( E @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ c_COMBB ) ) @ ( E @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Olist_ONil @ ( E @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3331]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib__neg) ).
thf(6949,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(2528,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) ).
thf(14647,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2528]) ).
thf(1434,axiom,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__code__numeral__code) ).
thf(10200,plain,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).
thf(2617,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).
thf(15030,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2617]) ).
thf(45264,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
!= ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) ) )
| ( ( v_c @ ( c_Int_OPls @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(paramod_ordered,[status(thm)],[8226,39009]) ).
thf(45471,plain,
! [A: $i] :
( ( c_Int_OPls != A )
| ( ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( c_Int_OPls @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[45264]) ).
thf(45792,plain,
( ( ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( v_c @ ( c_Int_OPls @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[45471]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
<=> ( A
= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__is__Nil__conv) ).
thf(7233,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( D @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
=> ( A
= ( D @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1081,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__minus1) ).
thf(8814,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(3022,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( A @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I1) ).
thf(16617,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( A @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3022]) ).
thf(1307,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(9733,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(1453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult) ).
thf(10334,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(3577,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Fun_Oid @ ( B @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__o) ).
thf(18836,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Fun_Oid @ ( B @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3577]) ).
thf(988,axiom,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
thf(8470,plain,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(1021,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(8580,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__diff2) ).
thf(5067,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(4627,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).
thf(22895,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4627]) ).
thf(2488,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
thf(14481,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2488]) ).
thf(4502,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) ) )
<=> ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).
thf(22419,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) ) )
=> ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4502]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(7134,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(1936,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(12231,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1936]) ).
thf(3346,axiom,
tc_Int_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
thf(17854,plain,
tc_Int_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3346]) ).
thf(3678,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( E @ ( F @ ( G @ ( H @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ! [I: $i] :
( ( I @ ( D @ hAPP ) @ ( E @ hAPP ) )
= ( I @ ( A @ hAPP ) @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(19217,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( E @ ( F @ ( G @ ( H @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ! [I: $i] :
( ( I @ ( D @ hAPP ) @ ( E @ hAPP ) )
= ( I @ ( A @ hAPP ) @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3678]) ).
thf(334,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ c_Int_Opred )
= ( A @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Bit1) ).
thf(5923,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 @ c_Int_Opred )
= ( A @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(2700,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff) ).
thf(15320,plain,
! [A: $i,B: $i] :
( ( ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2700]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I2_J) ).
thf(6581,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(3244,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__iff) ).
thf(17468,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( C @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( E @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3244]) ).
thf(3821,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__Int) ).
thf(19797,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3821]) ).
thf(1494,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(10480,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494]) ).
thf(1135,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__transpose) ).
thf(9025,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(3116,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib2) ).
thf(16977,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3116]) ).
thf(709,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
thf(7440,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(3731,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
thf(19440,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3731]) ).
thf(3612,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__pos__nat__iff) ).
thf(18953,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3612]) ).
thf(4199,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__iff__inf) ).
thf(21289,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4199]) ).
thf(3850,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_OCollect @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
thf(19949,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_OCollect @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3850]) ).
thf(3481,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( F @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( G @ c_List_Olexord ) @ ( A @ ( E @ ( G @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( G @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( G @ tc_List_Olist @ ( G @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ tc_List_Olist @ ( G @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).
thf(18418,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( F @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( G @ c_List_Olexord ) @ ( A @ ( E @ ( G @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( G @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( G @ tc_List_Olist @ ( G @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ tc_List_Olist @ ( G @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3481]) ).
thf(1542,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__neg) ).
thf(10709,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542]) ).
thf(3893,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__empty ) ) ) )
= ( D @ c_New__DSequence_Opos__empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__empty__def) ).
thf(20105,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__empty ) ) ) )
= ( D @ c_New__DSequence_Opos__empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3893]) ).
thf(3497,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge1) ).
thf(18494,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3497]) ).
thf(1051,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(8684,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(3605,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( D @ ( H @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( E @ hAPP ) @ ( C @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ hAPP ) @ ( C @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( F @ hAPP ) @ ( C @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( C @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).
thf(18927,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( D @ ( H @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( E @ hAPP ) @ ( C @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ hAPP ) @ ( C @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( F @ hAPP ) @ ( C @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( C @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3605]) ).
thf(310,axiom,
! [A: $i] :
( ( A @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__nat) ).
thf(5831,plain,
! [A: $i] :
( ( A @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(2152,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__minus__add__max) ).
thf(13033,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2152]) ).
thf(1651,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ! [D: $i] :
( ( ( D @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ( D @ ( B @ c_List_Olinorder__class_Osorted ) )
& ( ( D @ ( B @ c_List_Oset @ hAPP ) )
= A ) )
=> ( D = C ) )
& ( C @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ( C @ ( B @ c_List_Olinorder__class_Osorted ) )
& ( ( C @ ( B @ c_List_Oset @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__sorted__distinct__unique) ).
thf(11124,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ! [D: $i] :
( ( ( D @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ( D @ ( B @ c_List_Olinorder__class_Osorted ) )
& ( ( D @ ( B @ c_List_Oset @ hAPP ) )
= A ) )
=> ( D = C ) )
& ( C @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ( C @ ( B @ c_List_Olinorder__class_Osorted ) )
& ( ( C @ ( B @ c_List_Oset @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651]) ).
thf(2969,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).
thf(16400,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2969]) ).
thf(4049,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
thf(20641,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4049]) ).
thf(2173,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Predicate_OPowp ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__def) ).
thf(13125,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Predicate_OPowp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Predicate_OPowp ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2173]) ).
thf(2323,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
thf(13755,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2323]) ).
thf(1835,axiom,
tc_HOL_Obool @ class_Lattices_Oboolean__algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
thf(11851,plain,
tc_HOL_Obool @ class_Lattices_Oboolean__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1835]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__1) ).
thf(5050,plain,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(2940,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__nat) ).
thf(16278,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2940]) ).
thf(2281,axiom,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ! [B: $i] :
( ( A @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__eq__0__nat__iff__nat) ).
thf(13561,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [B: $i] :
( ( A @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2281]) ).
thf(1257,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__rtrancl) ).
thf(9521,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(3695,axiom,
( c_Wellfounded_Opred__nat
= ( c_Nat_OSuc @ ( c_fequal @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__nat__def) ).
thf(19296,plain,
( c_Wellfounded_Opred__nat
= ( c_Nat_OSuc @ ( c_fequal @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3695]) ).
thf(2233,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( tc_Int_Oint @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_simp__from__to) ).
thf(13363,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( tc_Int_Oint @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2233]) ).
thf(2948,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist__all ) ) )
<=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__iff__raw) ).
thf(16313,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Olist__all ) ) ) )
& ( ( A @ ( B @ ( C @ c_List_Olist__all ) ) )
=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2948]) ).
thf(4478,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_OPow @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__empty) ).
thf(22340,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_OPow @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4478]) ).
thf(3578,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( B @ c_COMBK ) @ hAPP ) @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant) ).
thf(18839,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( B @ c_COMBK ) @ hAPP ) @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3578]) ).
thf(3127,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__is__surj) ).
thf(17028,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3127]) ).
thf(1485,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( B @ ( C @ ( D @ c_List_Oremove1 ) ) @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__map__remove1) ).
thf(10435,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( B @ ( C @ ( D @ c_List_Oremove1 ) ) @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485]) ).
thf(3029,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I5_J) ).
thf(16649,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3029]) ).
thf(4625,axiom,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(22890,plain,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4625]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__mult) ).
thf(5271,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(3930,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [H: $i] :
( ( D @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( H @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__E) ).
thf(20237,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [H: $i] :
( ( D @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( H @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3930]) ).
thf(2705,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( B @ c_Relation_ORange ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] : ( A @ ( C @ ( E @ ( D @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__iff) ).
thf(15348,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( A @ ( C @ ( E @ ( D @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_Relation_ORange ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ ( B @ c_Relation_ORange ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] : ( A @ ( C @ ( E @ ( D @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2705]) ).
thf(2526,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).
thf(14642,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2526]) ).
thf(1344,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Osym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Id__on) ).
thf(9852,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Osym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(2371,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( B @ hAPP ) @ ( C @ c_Wellfounded_OwfP ) )
=> ( ! [D: $i,E: $i] :
( ( ( D @ ( B @ hAPP ) )
!= ( E @ ( B @ hAPP ) ) )
=> ( ( E @ ( B @ hAPP ) @ ( C @ ( C @ c_Predicate_ORangeP ) ) @ ( D @ ( B @ hAPP ) @ ( C @ ( C @ c_Predicate_ODomainP ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_OwfP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__SUP) ).
thf(13920,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( B @ hAPP ) @ ( C @ c_Wellfounded_OwfP ) )
=> ( ! [D: $i,E: $i] :
( ( ( D @ ( B @ hAPP ) )
!= ( E @ ( B @ hAPP ) ) )
=> ( ( E @ ( B @ hAPP ) @ ( C @ ( C @ c_Predicate_ORangeP ) ) @ ( D @ ( B @ hAPP ) @ ( C @ ( C @ c_Predicate_ODomainP ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_OwfP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2371]) ).
thf(1591,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__all ) ) )
<=> ( ( A @ ( C @ ( D @ c_List_Olist__all ) ) )
& ( B @ ( C @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__simps_I1_J) ).
thf(10874,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_List_Olist__all ) ) )
& ( B @ ( C @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__all ) ) ) )
& ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__all ) ) )
=> ( ( A @ ( C @ ( D @ c_List_Olist__all ) ) )
& ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591]) ).
thf(15,axiom,
( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
= ( tc_Int_Oint @ c_Fun_Oid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__eq__id) ).
thf(4768,plain,
( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
= ( tc_Int_Oint @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4769,plain,
( ( tc_Int_Oint @ c_Fun_Oid )
= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) ),
inference(lifteq,[status(thm)],[4768]) ).
thf(4248,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).
thf(21497,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4248]) ).
thf(4061,axiom,
! [A: $i] :
( ( A @ c_Int_Oint__ge__less__than2 )
= ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__ge__less__than2__def) ).
thf(20673,plain,
! [A: $i] :
( ( A @ c_Int_Oint__ge__less__than2 )
= ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4061]) ).
thf(2918,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).
thf(16189,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2918]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__triv) ).
thf(5799,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(1875,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) )
= ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conj__eq) ).
thf(12011,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) )
= ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1875]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Opdivmod ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__def) ).
thf(4946,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Opdivmod ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(3155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).
thf(17130,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3155]) ).
thf(2661,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
thf(15195,plain,
! [A: $i,B: $i] :
( ( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2661]) ).
thf(2306,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__eq__iff) ).
thf(13685,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2306]) ).
thf(3168,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ ( C @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfE__pf) ).
thf(17199,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ ( C @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3168]) ).
thf(2047,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ohom__commute) ).
thf(12636,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2047]) ).
thf(3592,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ c_Enum_On__lists ) ) )
= ( B @ tc_List_Olist @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__lists_Osimps_I1_J) ).
thf(18884,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ c_Enum_On__lists ) ) )
= ( B @ tc_List_Olist @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3592]) ).
thf(2137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI) ).
thf(12964,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2137]) ).
thf(4369,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_OremoveAll ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__removeAll) ).
thf(21974,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_OremoveAll ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4369]) ).
thf(3936,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( C @ ( D @ c_Relation_OImage ) ) @ hAPP ) )
= ( B @ ( tc_HOL_Obool @ ( C @ ( D @ c_COMBC ) ) @ hAPP ) @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Collect__split) ).
thf(20254,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( C @ ( D @ c_Relation_OImage ) ) @ hAPP ) )
= ( B @ ( tc_HOL_Obool @ ( C @ ( D @ c_COMBC ) ) @ hAPP ) @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3936]) ).
thf(749,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
<=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL ) )
& ! [C: $i] :
( ( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( C @ ( B @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__nat) ).
thf(7622,plain,
! [A: $i,B: $i] :
( ( ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL ) )
& ! [C: $i] :
( ( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( C @ ( B @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL ) )
& ! [C: $i] :
( ( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( C @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(228,axiom,
! [A: $i] :
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( A @ c_Code__Numeral_OSuc__code__numeral @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__code__numeral__minus__one) ).
thf(5535,plain,
! [A: $i] :
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( A @ c_Code__Numeral_OSuc__code__numeral @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(3585,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( F @ ( F @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( F @ ( F @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__I) ).
thf(18863,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( F @ ( F @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_HOL_Obool @ ( F @ ( F @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3585]) ).
thf(799,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod) ).
thf(7795,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(2920,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
thf(16194,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2920]) ).
thf(3291,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff) ).
thf(17654,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3291]) ).
thf(1394,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(10044,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zminus) ).
thf(7218,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1940,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Olist_OCons @ ( D @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ c_COMBB ) ) @ ( D @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Olist_ONil @ ( D @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons1) ).
thf(12242,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Olist_OCons @ ( D @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ c_COMBB ) ) @ ( D @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Olist_ONil @ ( D @ ( D @ ( E @ tc_prod ) @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1940]) ).
thf(2139,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
thf(12969,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2139]) ).
thf(943,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(8318,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) )
= ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( D @ c_List_Olist_ONil @ ( D @ c_List_Orotate1 @ hAPP ) )
= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__simps) ).
thf(5185,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) )
= ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( D @ c_List_Olist_ONil @ ( D @ c_List_Orotate1 @ hAPP ) )
= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1068,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oidem) ).
thf(8767,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(2549,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).
thf(14743,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2549]) ).
thf(3465,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).
thf(18350,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3465]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).
thf(5546,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(2784,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
<=> ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) )
=> ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_periodic__finite__ex) ).
thf(15641,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) )
=> ( ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) )
& ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2784]) ).
thf(3361,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Collect__eq) ).
thf(17905,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3361]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__add )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ ( B @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__0) ).
thf(5039,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__add )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ ( B @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1377,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(9984,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(2781,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert__distrib) ).
thf(15630,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2781]) ).
thf(707,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__code__numeral__def) ).
thf(7425,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(2039,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ( ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
| ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__Un) ).
thf(12592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
| ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
| ? [E: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2039]) ).
thf(2403,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ c_Relation_ORange ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__rtrancl) ).
thf(14076,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ c_Relation_ORange ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2403]) ).
thf(2465,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).
thf(14384,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2465]) ).
thf(2294,axiom,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olexord ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).
thf(13633,plain,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olexord ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2294]) ).
thf(2418,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Orderings_Olinorder )
=> ( ( ~ ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key_Osimps_I2_J) ).
thf(14144,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Orderings_Olinorder )
=> ( ( ~ ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2418]) ).
thf(4539,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).
thf(22577,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4539]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power2) ).
thf(6385,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(3317,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__0L) ).
thf(17744,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3317]) ).
thf(1010,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( A @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__refl) ).
thf(8549,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( A @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(2952,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__comp) ).
thf(16334,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2952]) ).
thf(212,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).
thf(5471,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1692,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__nth__mono) ).
thf(11301,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).
thf(2973,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
thf(16415,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2973]) ).
thf(4202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ouminus )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__Compl__def) ).
thf(21309,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ouminus )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4202]) ).
thf(2991,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).
thf(16515,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2991]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__code__numeral__code) ).
thf(6357,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(4610,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Un) ).
thf(22841,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4610]) ).
thf(2302,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).
thf(13673,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2302]) ).
thf(891,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
thf(8152,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(1889,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).
thf(12067,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1889]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__3) ).
thf(6667,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(935,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__special_I1_J) ).
thf(8286,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(916,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Otl @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__tl) ).
thf(8227,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Otl @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(2069,axiom,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).
thf(12716,plain,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2069]) ).
thf(1884,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I6_J) ).
thf(12053,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1884]) ).
thf(853,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
thf(7983,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(3596,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__absorb) ).
thf(18899,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3596]) ).
thf(1984,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I4_J) ).
thf(12401,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1984]) ).
thf(1634,axiom,
! [A: $i] : ( A @ c_Relation_OId @ ( A @ ( A @ c_Relation_Osingle__valued ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id) ).
thf(11060,plain,
! [A: $i] : ( A @ c_Relation_OId @ ( A @ ( A @ c_Relation_Osingle__valued ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634]) ).
thf(2391,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( E @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greaterThanLessThan) ).
thf(14010,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( E @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2391]) ).
thf(1038,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
thf(8629,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).
thf(6532,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(240,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel) ).
thf(5595,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(3684,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Un) ).
thf(19234,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3684]) ).
thf(1016,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).
thf(8566,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1860,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( D @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ ( c_fequal @ ( tc_HOL_Obool @ ( E @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( E @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( F @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
& ( ( D @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ ( c_fequal @ ( tc_HOL_Obool @ ( E @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( E @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( E @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( F @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__gen__delta) ).
thf(11951,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( D @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ ( c_fequal @ ( tc_HOL_Obool @ ( E @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( E @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( F @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
& ( ( D @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ ( c_fequal @ ( tc_HOL_Obool @ ( E @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( E @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( E @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( F @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1860]) ).
thf(3943,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Wellfounded_Oaccp ) @ ( A @ ( C @ c_Wellfounded_Oaccp ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__subset) ).
thf(20283,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Wellfounded_Oaccp ) @ ( A @ ( C @ c_Wellfounded_Oaccp ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3943]) ).
thf(2166,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oclosed) ).
thf(13093,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2166]) ).
thf(1094,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(8877,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(3274,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).
thf(17590,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3274]) ).
thf(1907,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
thf(12128,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1907]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OnegDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OnegDivAlg ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Divides_OnegDivAlg ) @ ( A @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OnegDivAlg ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Opsimps) ).
thf(5331,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OnegDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OnegDivAlg ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Divides_OnegDivAlg ) @ ( A @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OnegDivAlg ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( B @ ( C @ c_List_Orev @ hAPP ) @ ( A @ ( C @ c_List_Orev @ hAPP ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__append) ).
thf(5282,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( B @ ( C @ c_List_Orev @ hAPP ) @ ( A @ ( C @ c_List_Orev @ hAPP ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(4233,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( B @ c_Relation_ORange ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
~ ( A @ ( C @ ( E @ ( D @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeE) ).
thf(21433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( B @ c_Relation_ORange ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
~ ( A @ ( C @ ( E @ ( D @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4233]) ).
thf(2748,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oord )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__iff) ).
thf(15517,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oord )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2748]) ).
thf(3105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(16945,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3105]) ).
thf(2020,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
thf(12524,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2020]) ).
thf(4410,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left) ).
thf(22113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4410]) ).
thf(957,axiom,
! [A: $i,B: $i] :
( ( A @ c_COMBI @ ( B @ c_COMBI @ ( A @ ( A @ ( B @ ( B @ c_Product__Type_Omap__pair ) ) ) ) ) )
= ( A @ ( B @ tc_prod ) @ c_Fun_Oid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Oidentity) ).
thf(8359,plain,
! [A: $i,B: $i] :
( ( A @ c_COMBI @ ( B @ c_COMBI @ ( A @ ( A @ ( B @ ( B @ c_Product__Type_Omap__pair ) ) ) ) ) )
= ( A @ ( B @ tc_prod ) @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Ofilter ) @ hAPP ) ) )
<=> ? [F: $i,G: $i] :
( ( C
= ( G @ ( B @ ( E @ c_List_Ofilter ) @ hAPP ) ) )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ! [H: $i] :
( ( F @ ( E @ c_List_Oset @ hAPP ) @ ( H @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( H @ ( B @ hAPP ) @ hBOOL ) )
& ( A
= ( G @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__filter__iff) ).
thf(6091,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i,G: $i] :
( ( C
= ( G @ ( B @ ( E @ c_List_Ofilter ) @ hAPP ) ) )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ! [H: $i] :
( ( F @ ( E @ c_List_Oset @ hAPP ) @ ( H @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( H @ ( B @ hAPP ) @ hBOOL ) )
& ( A
= ( G @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
=> ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Ofilter ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Ofilter ) @ hAPP ) ) )
=> ? [F: $i,G: $i] :
( ( C
= ( G @ ( B @ ( E @ c_List_Ofilter ) @ hAPP ) ) )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ! [H: $i] :
( ( F @ ( E @ c_List_Oset @ hAPP ) @ ( H @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( H @ ( B @ hAPP ) @ hBOOL ) )
& ( A
= ( G @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(3870,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J) ).
thf(20019,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3870]) ).
thf(4237,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Osubset__idem) ).
thf(21460,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4237]) ).
thf(3259,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__setprod) ).
thf(17525,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3259]) ).
thf(1997,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I4_J) ).
thf(12451,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1997]) ).
thf(4298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( ( C @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( E @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( E @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( ( E @ ( B @ hAPP ) )
= A )
& ( C @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__intermed__int__val) ).
thf(21682,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( ( C @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( E @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( E @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( ( E @ ( B @ hAPP ) )
= A )
& ( C @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4298]) ).
thf(2631,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fdisj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__compr__raw) ).
thf(15081,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fdisj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2631]) ).
thf(1439,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Transitive__Closure_Ortrancl ) )
= ( A @ c_Relation_OId ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__empty) ).
thf(10215,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Transitive__Closure_Ortrancl ) )
= ( A @ c_Relation_OId ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).
thf(3075,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
thf(16823,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3075]) ).
thf(4762,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ class_Rings_Olinordered__idom ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ class_Rings_Olinordered__idom ) ) ),
inference(cnf,[status(esa)],[4761]) ).
thf(4764,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ class_Rings_Olinordered__idom ) ),
inference(cnfConj,[status(thm)],[4762]) ).
thf(1323,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__commute) ).
thf(9776,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(612,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( F @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( E @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__simp) ).
thf(7094,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( F @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( E @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(2889,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I9_J) ).
thf(16065,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2889]) ).
thf(4001,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) )
= ( A @ ( C @ c_Set_OCollect @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_OCollect @ hAPP ) @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetCompr__Sigma__eq) ).
thf(20462,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) )
= ( A @ ( C @ c_Set_OCollect @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_OCollect @ hAPP ) @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4001]) ).
thf(3180,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mod__geq) ).
thf(17236,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3180]) ).
thf(3737,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( A @ ( B @ ( F @ hAPP ) @ ( D @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( F @ hAPP ) @ ( D @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ ( F @ hAPP ) @ ( D @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ hAPP ) @ ( D @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp) ).
thf(19466,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( A @ ( B @ ( F @ hAPP ) @ ( D @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( F @ hAPP ) @ ( D @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ ( F @ hAPP ) @ ( D @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ hAPP ) @ ( D @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3737]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olast ) )
= ( B @ ( A @ c_List_Ohd @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__rev) ).
thf(5207,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olast ) )
= ( B @ ( A @ c_List_Ohd @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(3282,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).
thf(17628,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3282]) ).
thf(2422,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
thf(14161,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2422]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__minus) ).
thf(5314,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(2854,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_OPow @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__def) ).
thf(15936,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_OPow @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2854]) ).
thf(1247,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__le) ).
thf(9496,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(759,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Cons) ).
thf(7671,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(2482,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hom__fold1__commute) ).
thf(14461,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2482]) ).
thf(2511,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ? [C: $i,D: $i] :
( A
= ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( D @ ( B @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__conv__nat__seg__image) ).
thf(14587,plain,
! [A: $i,B: $i] :
( ( ? [C: $i,D: $i] :
( A
= ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( D @ ( B @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [C: $i,D: $i] :
( A
= ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( D @ ( B @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2511]) ).
thf(4445,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
thf(22227,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4445]) ).
thf(3410,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( F @ c_List_Olistrel1 ) @ ( F @ c_List_Olist_ONil @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ c_List_Olist_ONil @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( B @ ( D @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( F @ c_List_Olistrel1 ) @ ( C @ ( E @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
thf(18124,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( B @ ( D @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( F @ c_List_Olistrel1 ) @ ( C @ ( E @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( F @ c_List_Olistrel1 ) @ ( F @ c_List_Olist_ONil @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ c_List_Olist_ONil @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( F @ c_List_Olistrel1 ) @ ( F @ c_List_Olist_ONil @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ c_List_Olist_ONil @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( D @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( F @ c_List_Olistrel1 ) @ ( C @ ( E @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3410]) ).
thf(997,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decr__lemma) ).
thf(8497,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(2618,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta_H) ).
thf(15036,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2618]) ).
thf(3810,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Int__subset) ).
thf(19762,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3810]) ).
thf(587,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Ois__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).
thf(7006,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Ois__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(4604,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i] :
( ( G @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( A @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( G @ ( c_fequal @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ ( tc_Com_Ostate @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( E @ ( D @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_escape) ).
thf(22822,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i] :
( ( G @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( A @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( G @ ( c_fequal @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ ( tc_Com_Ostate @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( E @ ( D @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4604]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__Nil) ).
thf(5735,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(1809,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oappend @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( A @ ( C @ c_List_Oconcat ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__conv__concat) ).
thf(11750,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oappend @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( A @ ( C @ c_List_Oconcat ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1809]) ).
thf(1678,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
=> ( ( A @ c_Orderings_Oord__class_Omin )
= ( A @ c_Orderings_Oord__class_Oless__eq @ ( A @ c_Orderings_Oord_Omin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ord__min) ).
thf(11237,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
=> ( ( A @ c_Orderings_Oord__class_Omin )
= ( A @ c_Orderings_Oord__class_Oless__eq @ ( A @ c_Orderings_Oord_Omin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678]) ).
thf(1832,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
thf(11841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1832]) ).
thf(1004,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zero) ).
thf(8524,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(4098,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Wellfounded_Omax__extp ) ) ) )
<=> ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Osimps) ).
thf(20864,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Wellfounded_Omax__extp ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Wellfounded_Omax__extp ) ) ) )
=> ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4098]) ).
thf(3094,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_peek__and__def) ).
thf(16909,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( A @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3094]) ).
thf(2104,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).
thf(12825,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2104]) ).
thf(3960,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( D @ ( E @ tc_prod ) @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__cartesian__product) ).
thf(20330,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( D @ ( E @ tc_prod ) @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3960]) ).
thf(3001,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__infI) ).
thf(16553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3001]) ).
thf(3833,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupto ) )
= ( tc_Int_Oint @ c_List_Olist_ONil ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupto ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupto ) @ ( B @ ( tc_Int_Oint @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto_Osimps) ).
thf(19843,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupto ) )
= ( tc_Int_Oint @ c_List_Olist_ONil ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupto ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupto ) @ ( B @ ( tc_Int_Oint @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3833]) ).
thf(3062,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( G @ ( H @ ( I @ ( J @ c_Set_Oimage ) ) @ hAPP ) )
= F )
=> ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= A )
=> ( ( B @ ( J @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( G @ ( E @ ( J @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( H @ ( D @ ( E @ ( I @ ( J @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( D @ ( I @ tc_prod ) @ ( E @ ( J @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( I @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( F @ ( D @ ( I @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__surj__on) ).
thf(16782,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( G @ ( H @ ( I @ ( J @ c_Set_Oimage ) ) @ hAPP ) )
= F )
=> ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= A )
=> ( ( B @ ( J @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( G @ ( E @ ( J @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( H @ ( D @ ( E @ ( I @ ( J @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( D @ ( I @ tc_prod ) @ ( E @ ( J @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( I @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( F @ ( D @ ( I @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3062]) ).
thf(39014,plain,
c_Int_OPls @ c_Nat__Transfer_Ois__nat,
inference(rewrite,[status(thm)],[7518,7678]) ).
thf(4018,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(20518,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4018]) ).
thf(2914,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Pow__iff) ).
thf(16174,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2914]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add1__eq) ).
thf(5784,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(4799,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
| ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Oring__1 ) ),
inference(cnfConj,[status(thm)],[4797]) ).
thf(4801,plain,
! [B: $i,A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Oring__1 )
| ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4799]) ).
thf(44167,plain,
! [B: $i,A: $i] :
( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Oring__1 )
| ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ) ),
inference(rewrite,[status(thm)],[4801,7678]) ).
thf(3711,axiom,
! [A: $i,B: $i] :
( ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) ) )
<=> ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff2) ).
thf(19352,plain,
! [A: $i,B: $i] :
( ( ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) ) ) )
& ( ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) ) )
=> ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3711]) ).
thf(1820,axiom,
! [A: $i] :
( ( ( A @ class_Orderings_Olinorder )
& ( A @ class_Lattices_Osemilattice__inf ) )
=> ( ( A @ c_Lattices_Osemilattice__inf__class_Oinf )
= ( A @ c_Orderings_Oord__class_Omin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__min) ).
thf(11792,plain,
! [A: $i] :
( ( ( A @ class_Orderings_Olinorder )
& ( A @ class_Lattices_Osemilattice__inf ) )
=> ( ( A @ c_Lattices_Osemilattice__inf__class_Oinf )
= ( A @ c_Orderings_Oord__class_Omin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1820]) ).
thf(4525,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__triv) ).
thf(22523,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4525]) ).
thf(1813,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
thf(11765,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( ( B = A )
=> ( D = C ) )
& ( ( D = C )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1813]) ).
thf(2992,axiom,
! [A: $i] :
~ ( A @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(16518,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2992]) ).
thf(856,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( A @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__comp) ).
thf(8010,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( A @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(3784,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).
thf(19666,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3784]) ).
thf(3216,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less) ).
thf(17369,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3216]) ).
thf(2393,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ ( E @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).
thf(14027,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ ( E @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2393]) ).
thf(2835,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__conv__Nil) ).
thf(15857,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2835]) ).
thf(3474,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_List_Olistrel ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).
thf(18399,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_List_Olistrel ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3474]) ).
thf(2141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).
thf(12979,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2141]) ).
thf(696,axiom,
! [A: $i] :
( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).
thf(7394,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(1478,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__2) ).
thf(10416,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(1427,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) )
= ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__insort) ).
thf(10176,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) )
= ( A @ ( B @ ( C @ c_COMBI @ ( C @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(2014,axiom,
tc_Int_Oint @ class_Groups_Ouminus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
thf(12509,plain,
tc_Int_Oint @ class_Groups_Ouminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2014]) ).
thf(1550,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(10741,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550]) ).
thf(1499,axiom,
c_Int_OPls @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I23_J) ).
thf(10505,plain,
c_Int_OPls @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).
thf(3189,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oid @ ( A @ ( A @ c_Fun_Obij__betw ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__id) ).
thf(17260,plain,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oid @ ( A @ ( A @ c_Fun_Obij__betw ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3189]) ).
thf(783,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).
thf(7746,plain,
tc_Code__Numeral_Ocode__numeral @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(963,axiom,
! [A: $i] :
( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__of__nat) ).
thf(8376,plain,
! [A: $i] :
( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(3701,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(19321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3701]) ).
thf(940,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).
thf(8301,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(3495,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).
thf(18487,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3495]) ).
thf(4557,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
thf(22636,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4557]) ).
thf(255,axiom,
! [A: $i] :
( ( ( A @ class_Rings_Olinordered__idom )
& ( A @ class_Int_Onumber__ring ) )
=> ( ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__one) ).
thf(5634,plain,
! [A: $i] :
( ( ( A @ class_Rings_Olinordered__idom )
& ( A @ class_Int_Onumber__ring ) )
=> ( ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1374,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(9967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(1398,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__number__of__lemma) ).
thf(10056,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ ( C @ c_List_Olinorder__class_Osort__key ) ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__sort) ).
thf(5580,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ ( C @ c_List_Olinorder__class_Osort__key ) ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(2856,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1_H) ).
thf(15941,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2856]) ).
thf(19057,plain,
( ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin )
= ( tc_Nat_Onat @ c_Lattices_Osemilattice__inf__class_Oinf ) ),
inference(lifteq,[status(thm)],[19056]) ).
thf(3760,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).
thf(19570,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3760]) ).
thf(1419,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(10140,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(1287,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( B @ c_List_Onth @ ( B @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__transpose) ).
thf(9670,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( B @ c_List_Onth @ ( B @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(3904,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff) ).
thf(20141,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3904]) ).
thf(4320,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__natinterval__difff) ).
thf(21783,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4320]) ).
thf(3456,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Inter__image) ).
thf(18309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3456]) ).
thf(1870,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Onat__set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).
thf(11996,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Onat__set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1870]) ).
thf(4596,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL )
<=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
thf(22786,plain,
! [A: $i,B: $i] :
( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4596]) ).
thf(3368,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__supI2) ).
thf(17935,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3368]) ).
thf(3798,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int2) ).
thf(19715,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3798]) ).
thf(485,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_List_Olist_ONil )
= ( A @ ( B @ c_List_Oremdups ) ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__eq__nil__right__iff) ).
thf(6585,plain,
! [A: $i,B: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( ( B @ c_List_Olist_ONil )
= ( A @ ( B @ c_List_Oremdups ) ) ) )
& ( ( ( B @ c_List_Olist_ONil )
= ( A @ ( B @ c_List_Oremdups ) ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(2246,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( G @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( G @ ( E @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(13417,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( G @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( G @ ( E @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2246]) ).
thf(974,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Relation_OField @ hAPP ) )
= ( A @ ( B @ c_Relation_OField @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__converse) ).
thf(8419,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Relation_OField @ hAPP ) )
= ( A @ ( B @ c_Relation_OField @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(4181,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__Un2) ).
thf(21222,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4181]) ).
thf(1674,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastAtMost__int) ).
thf(11222,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1674]) ).
thf(3238,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le2) ).
thf(17448,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3238]) ).
thf(2903,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( A @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I6_J) ).
thf(16133,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( A @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2903]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc__number__of) ).
thf(6024,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(3584,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ hAPP ) )
= A )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).
thf(18859,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ hAPP ) )
= A )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3584]) ).
thf(1267,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups_Osimps_I1_J) ).
thf(9560,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(3876,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [F: $i] :
( ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__iff) ).
thf(20036,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3876]) ).
thf(1893,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).
thf(12082,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1893]) ).
thf(703,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power__minus__one) ).
thf(7415,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(2874,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ c_List_Onth @ hAPP ) @ ( B @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__conv__card) ).
thf(16000,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ c_List_Onth @ hAPP ) @ ( B @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2874]) ).
thf(3203,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I4_J) ).
thf(17312,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3203]) ).
thf(2099,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( G @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ c_List_Olistrel ) @ ( G @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons1) ).
thf(12806,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( G @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ c_List_Olistrel ) @ ( G @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2099]) ).
thf(3046,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinsert) ).
thf(16718,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3046]) ).
thf(2289,axiom,
! [A: $i] :
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__less__0__conv) ).
thf(13609,plain,
! [A: $i] :
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2289]) ).
thf(1407,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ c_List_Oset @ hAPP ) @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( E @ ( B @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__insort__key) ).
thf(10088,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ c_List_Oset @ hAPP ) @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( E @ ( B @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).
thf(1990,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less) ).
thf(12428,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1990]) ).
thf(933,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
thf(8276,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(11661,plain,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(polarity_switch,[status(thm)],[11660]) ).
thf(11662,plain,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(lifteq,[status(thm)],[11661]) ).
thf(33132,plain,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ),
inference(rewrite,[status(thm)],[11662,4775]) ).
thf(1600,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__times) ).
thf(10921,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600]) ).
thf(1791,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
thf(11686,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1791]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
thf(7519,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(1506,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ ( B @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(10532,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ ( B @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506]) ).
thf(2798,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).
thf(15700,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2798]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( A @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
thf(7783,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( A @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1483,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(10429,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(4241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I8_J) ).
thf(21469,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4241]) ).
thf(4291,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__idem) ).
thf(21664,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4291]) ).
thf(2928,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__delta_H) ).
thf(16226,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2928]) ).
thf(2916,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(16182,plain,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2916]) ).
thf(4476,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_OPow @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__UNIV) ).
thf(22335,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_OPow @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4476]) ).
thf(2051,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Nat__Transfer_Otsub ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
thf(12651,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Nat__Transfer_Otsub ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2051]) ).
thf(4058,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Osublist ) ) )
= ( A @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( B @ ( D @ c_List_Osublist ) ) @ ( D @ c_List_Olist_ONil @ ( D @ c_List_Olist_ONil @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__Cons) ).
thf(20664,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Osublist ) ) )
= ( A @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( B @ ( D @ c_List_Osublist ) ) @ ( D @ c_List_Olist_ONil @ ( D @ c_List_Olist_ONil @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4058]) ).
thf(752,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__pos) ).
thf(7643,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(2847,axiom,
! [A: $i] :
( ( A @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__UNIV) ).
thf(15902,plain,
! [A: $i] :
( ( A @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2847]) ).
thf(3919,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ ( B @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__mapI) ).
thf(20205,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ ( B @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3919]) ).
thf(3938,axiom,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [C: $i] :
( A
!= ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdE) ).
thf(20260,plain,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [C: $i] :
( A
!= ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3938]) ).
thf(2056,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Oset__Cons ) ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( B @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__Cons__sing__Nil) ).
thf(12668,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Oset__Cons ) ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( B @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2056]) ).
thf(4657,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Relation_ODomain ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty) ).
thf(23023,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Relation_ODomain ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4657]) ).
thf(1204,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(9312,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
thf(5506,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(3128,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Enum_Oproduct ) ) ) @ ( C @ ( D @ tc_prod ) @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_product__list__set) ).
thf(17031,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Enum_Oproduct ) ) ) @ ( C @ ( D @ tc_prod ) @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3128]) ).
thf(2980,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( E @ ( G @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( G @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( F @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__mono) ).
thf(16454,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( E @ ( G @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( G @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( F @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2980]) ).
thf(1057,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(8715,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(1742,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( B @ c_Random_Orange @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range) ).
thf(11508,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( B @ c_Random_Orange @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742]) ).
thf(1348,axiom,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Nat__Transfer_Ois__nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
thf(9867,plain,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Nat__Transfer_Ois__nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(1955,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty) ).
thf(12297,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1955]) ).
thf(1077,axiom,
! [A: $i,B: $i] :
( ( A @ c_Fun_Oid @ ( B @ c_Fun_Oid @ ( A @ ( A @ ( B @ ( B @ c_Product__Type_Omap__pair ) ) ) ) ) )
= ( A @ ( B @ tc_prod ) @ c_Fun_Oid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Oid) ).
thf(8799,plain,
! [A: $i,B: $i] :
( ( A @ c_Fun_Oid @ ( B @ c_Fun_Oid @ ( A @ ( A @ ( B @ ( B @ c_Product__Type_Omap__pair ) ) ) ) ) )
= ( A @ ( B @ tc_prod ) @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__diff__distrib__left) ).
thf(9614,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(1853,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Finite__Set_Ofold1Set ) ) @ ( C @ c_HOL_OThe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__def) ).
thf(11932,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Finite__Set_Ofold1Set ) ) @ ( C @ c_HOL_OThe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1853]) ).
thf(3309,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Rings_Osemiring__0 )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( G @ c_Groups_Otimes__class_Otimes @ ( F @ ( G @ ( G @ tc_fun ) @ ( G @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( G @ ( G @ c_COMBB ) ) @ ( F @ ( G @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ tc_fun ) @ ( G @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( G @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( G @ ( E @ ( F @ tc_prod ) @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( G @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( G @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( G @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( G @ c_Groups_Otimes__class_Otimes @ ( F @ ( G @ ( G @ tc_fun ) @ ( G @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( G @ ( G @ c_COMBB ) ) @ ( F @ ( G @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ tc_fun ) @ ( G @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( G @ c_COMBB ) ) @ ( G @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ c_COMBB ) ) @ ( G @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_COMBS ) ) @ ( G @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_HOL_OEx @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_HOL_OEx @ ( G @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ c_Set_OCollect @ hAPP ) @ ( G @ c_Fun_Oid @ ( G @ ( G @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).
thf(17712,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Rings_Osemiring__0 )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( G @ c_Groups_Otimes__class_Otimes @ ( F @ ( G @ ( G @ tc_fun ) @ ( G @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( G @ ( G @ c_COMBB ) ) @ ( F @ ( G @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ tc_fun ) @ ( G @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( G @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( G @ ( E @ ( F @ tc_prod ) @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( G @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( G @ ( F @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( G @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( G @ c_Groups_Otimes__class_Otimes @ ( F @ ( G @ ( G @ tc_fun ) @ ( G @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( G @ ( G @ c_COMBB ) ) @ ( F @ ( G @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ tc_fun ) @ ( G @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( G @ c_COMBB ) ) @ ( G @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ c_COMBB ) ) @ ( G @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_COMBS ) ) @ ( G @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_HOL_OEx @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_HOL_OEx @ ( G @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ c_Set_OCollect @ hAPP ) @ ( G @ c_Fun_Oid @ ( G @ ( G @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3309]) ).
thf(886,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Oacyclic ) )
<=> ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Oacyclic ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__insert) ).
thf(8135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Oacyclic ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Oacyclic ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Oacyclic ) )
=> ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Oacyclic ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(1361,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ ( C @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( E @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__zip) ).
thf(9903,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ ( C @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( E @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(803,axiom,
tc_HOL_Obool @ class_Lattices_Osemilattice__inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
thf(7810,plain,
tc_HOL_Obool @ class_Lattices_Osemilattice__inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(1400,axiom,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__trancl) ).
thf(10066,plain,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(4713,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
thf(23238,plain,
! [A: $i,B: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ! [C: $i] :
~ ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ! [C: $i] :
~ ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4713]) ).
thf(4033,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(20571,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4033]) ).
thf(538,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).
thf(6815,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(3468,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__insert) ).
thf(18367,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3468]) ).
thf(4108,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nitpick_Orefl_H ) )
<=> ! [C: $i] : ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
thf(20928,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Nitpick_Orefl_H ) ) )
& ( ( A @ ( B @ c_Nitpick_Orefl_H ) )
=> ! [C: $i] : ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4108]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(7607,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(6112,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(4435,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__bottom) ).
thf(22195,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4435]) ).
thf(3732,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons__Cons) ).
thf(19444,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3732]) ).
thf(254,axiom,
! [A: $i] :
( ( A @ class_Groups_Omonoid__add )
=> ( ( A @ c_List_Omonoid__add__class_Olistsum )
= ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oplus__class_Oplus @ ( A @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__foldl) ).
thf(5631,plain,
! [A: $i] :
( ( A @ class_Groups_Omonoid__add )
=> ( ( A @ c_List_Omonoid__add__class_Olistsum )
= ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oplus__class_Oplus @ ( A @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).
thf(5303,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(4092,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( E @ ( B @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) )
= ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( B @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__inv__distrib) ).
thf(20833,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( E @ ( B @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) )
= ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( B @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4092]) ).
thf(4703,axiom,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__singleton) ).
thf(23206,plain,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4703]) ).
thf(1598,axiom,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl__absorb) ).
thf(10898,plain,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598]) ).
thf(4490,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple__rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Orecs) ).
thf(22382,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple__rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4490]) ).
thf(2205,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__compat) ).
thf(13253,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2205]) ).
thf(4177,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I3_J) ).
thf(21205,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4177]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_List_Orev @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__rev__nth__mono) ).
thf(9047,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_List_Orev @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(4385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).
thf(22036,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4385]) ).
thf(3390,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Owf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__subset) ).
thf(18045,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3390]) ).
thf(2794,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb2) ).
thf(15686,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2794]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( C @ ( B @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( D @ tc_prod ) @ c_Wellfounded_Owf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex__prod) ).
thf(8171,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( C @ ( B @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( D @ tc_prod ) @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1515,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(10564,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515]) ).
thf(984,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__0) ).
thf(8461,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(4046,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).
thf(20628,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4046]) ).
thf(3748,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__lessThan) ).
thf(19520,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3748]) ).
thf(2512,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
thf(14595,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2512]) ).
thf(3690,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__absorb) ).
thf(19276,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3690]) ).
thf(322,axiom,
tc_Int_Oint @ class_Lattices_Osemilattice__inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).
thf(5880,plain,
tc_Int_Oint @ class_Lattices_Osemilattice__inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(1805,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
<=> ( B @ ( c_Int_Onat @ ( c_fequal @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__number__of) ).
thf(11733,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Int_Onat @ ( c_fequal @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
=> ( B @ ( c_Int_Onat @ ( c_fequal @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1805]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Obutlast ) @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__butlast) ).
thf(8254,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Obutlast ) @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(25020,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4735,25000]) ).
thf(25031,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= B )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[25020]) ).
thf(25048,plain,
! [A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( A @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[25031]) ).
thf(1175,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__int) ).
thf(9185,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(1155,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_COMBI @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__number__of__even) ).
thf(9118,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_COMBI @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(2564,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Set_OPow @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__top) ).
thf(14803,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Set_OPow @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2564]) ).
thf(3855,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Osym ) )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__def) ).
thf(19962,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ c_Relation_Osym ) ) )
& ( ( A @ ( B @ c_Relation_Osym ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3855]) ).
thf(1923,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition2) ).
thf(12182,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1923]) ).
thf(981,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
thf(8445,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(1448,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ c_List_Oreplicate ) ) @ ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( B @ ( A @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__replicate__commute) ).
thf(10316,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ c_List_Oreplicate ) ) @ ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( D @ c_List_Oreplicate ) ) @ ( B @ ( A @ ( D @ c_List_Oreplicate ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(3718,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_Enum_Osublists ) )
= ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ ( A @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublists_Osimps_I1_J) ).
thf(19385,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_Enum_Osublists ) )
= ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ ( A @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3718]) ).
thf(2377,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ ( F @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__apply) ).
thf(13945,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ ( F @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2377]) ).
thf(3438,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
thf(18250,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3438]) ).
thf(2284,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(13588,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2284]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__number__of__eq) ).
thf(4805,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(4602,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
<=> ( ( B = A )
& ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).
thf(22811,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( ( ( B = A )
& ( C = B ) )
=> ( ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
=> ( ( B = A )
& ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4602]) ).
thf(4563,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( A @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
& ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_derivs__insertD) ).
thf(22661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( A @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
& ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4563]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( B @ c_List_Oremdups ) @ ( B @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__remdups) ).
thf(7001,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( B @ c_List_Oremdups ) @ ( B @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__power) ).
thf(5222,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(2810,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).
thf(15740,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2810]) ).
thf(4292,axiom,
c_FunDef_Omax__weak @ ( c_FunDef_Omax__strict @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_FunDef_Oreduction__pair ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__rpair__set) ).
thf(21667,plain,
c_FunDef_Omax__weak @ ( c_FunDef_Omax__strict @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_FunDef_Oreduction__pair ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4292]) ).
thf(2484,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__bot )
=> ( ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__left) ).
thf(14471,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__bot )
=> ( ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2484]) ).
thf(2053,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__sup) ).
thf(12656,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2053]) ).
thf(3519,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__belowI) ).
thf(18570,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3519]) ).
thf(2503,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__in__set__insert) ).
thf(14540,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2503]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__dropWhile) ).
thf(8269,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(2228,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__diff__eq) ).
thf(13334,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2228]) ).
thf(2093,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
thf(12791,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2093]) ).
thf(1387,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).
thf(10019,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).
thf(4301,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep) ).
thf(21699,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4301]) ).
thf(4082,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__mono) ).
thf(20788,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4082]) ).
thf(1409,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Osym ) )
<=> ( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__conv__converse__eq) ).
thf(10098,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) )
= A )
=> ( A @ ( B @ c_Relation_Osym ) ) )
& ( ( A @ ( B @ c_Relation_Osym ) )
=> ( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(491,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( B @ ( tc_HOL_Obool @ c_COMBK ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( B @ c_Random_Oselect__weight ) )
= ( A @ ( B @ c_Random_Oselect__weight ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weigth__drop__zero) ).
thf(6604,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( B @ ( tc_HOL_Obool @ c_COMBK ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( B @ c_Random_Oselect__weight ) )
= ( A @ ( B @ c_Random_Oselect__weight ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(2191,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
thf(13210,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2191]) ).
thf(2231,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
thf(13348,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2231]) ).
thf(2397,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__subset__Cons) ).
thf(14048,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2397]) ).
thf(3828,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OAll @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ ( D @ c_COMBC ) ) @ hAPP ) @ ( D @ c_Set_OCollect @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__ball__eq) ).
thf(19824,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OAll @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ ( D @ c_COMBC ) ) @ hAPP ) @ ( D @ c_Set_OCollect @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3828]) ).
thf(687,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
thf(7362,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(4113,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__le__iff) ).
thf(20943,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4113]) ).
thf(1750,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).
thf(11531,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750]) ).
thf(3743,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
thf(19503,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3743]) ).
thf(2396,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).
thf(14042,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2396]) ).
thf(247,axiom,
tc_Int_Oint @ class_Rings_Ocomm__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
thf(5616,plain,
tc_Int_Oint @ class_Rings_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(1868,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( B @ ( D @ ( F @ ( E @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__iff) ).
thf(11979,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ ( D @ ( F @ ( E @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( B @ ( D @ ( F @ ( E @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1868]) ).
thf(4262,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( E @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageI2) ).
thf(21540,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( E @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4262]) ).
thf(1356,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__one) ).
thf(9890,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(1694,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__right) ).
thf(11306,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694]) ).
thf(2164,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oidem) ).
thf(13086,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2164]) ).
thf(1539,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Relation_OId @ ( B @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__O__R) ).
thf(10696,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Relation_OId @ ( B @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539]) ).
thf(2399,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__maxI1) ).
thf(14053,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2399]) ).
thf(1720,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(11406,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720]) ).
thf(2970,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
thf(16404,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2970]) ).
thf(2148,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD1) ).
thf(13018,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2148]) ).
thf(778,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).
thf(7731,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(4633,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
| ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).
thf(22935,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
| ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4633]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( B @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__append) ).
thf(5267,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( B @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(4196,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb2) ).
thf(21280,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4196]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( F @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( F @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( F @ ( E @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_Ofilter ) @ hAPP ) )
= ( C @ ( B @ ( E @ c_List_Ofilter ) @ hAPP ) @ ( A @ ( D @ ( F @ ( E @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__insort) ).
thf(6789,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( F @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( F @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( F @ ( E @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_Ofilter ) @ hAPP ) )
= ( C @ ( B @ ( E @ c_List_Ofilter ) @ hAPP ) @ ( A @ ( D @ ( F @ ( E @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(4661,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Obot )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).
thf(23040,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Obot )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4661]) ).
thf(2898,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( B @ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le1) ).
thf(16107,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( B @ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2898]) ).
thf(2189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Un) ).
thf(13204,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2189]) ).
thf(4005,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H) ).
thf(20479,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4005]) ).
thf(3929,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( D @ hAPP ) @ hBOOL )
=> ( E @ ( C @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( c_fequal @ ( A @ ( tc_HOL_Obool @ ( A @ c_COMBB ) ) @ ( A @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ ( A @ tc_fun ) @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( c_fconj @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ c_COMBS ) ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( A @ ( A @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__if__measure) ).
thf(20233,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( D @ hAPP ) @ hBOOL )
=> ( E @ ( C @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( c_fequal @ ( A @ ( tc_HOL_Obool @ ( A @ c_COMBB ) ) @ ( A @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ ( A @ tc_fun ) @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( c_fconj @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ c_COMBS ) ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( A @ ( A @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3929]) ).
thf(3706,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__into) ).
thf(19335,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3706]) ).
thf(3258,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Nat__Transfer_Otsub ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).
thf(17522,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Nat__Transfer_Otsub ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3258]) ).
thf(4529,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert) ).
thf(22541,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4529]) ).
thf(3445,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageD) ).
thf(18277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3445]) ).
thf(2598,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__atLeast) ).
thf(14925,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2598]) ).
thf(4023,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( D @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI) ).
thf(20539,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( D @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4023]) ).
thf(3771,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(19616,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3771]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
thf(6834,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(3749,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Id__on) ).
thf(19523,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3749]) ).
thf(1109,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( B @ c_Groups_Osgn__class_Osgn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__sgn) ).
thf(8932,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( B @ c_Groups_Osgn__class_Osgn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(185,axiom,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(5367,plain,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1942,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I44_J) ).
thf(12248,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1942]) ).
thf(2577,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Inf__iff) ).
thf(14850,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2577]) ).
thf(1316,axiom,
( c_FunDef_Opair__less
= ( c_Wellfounded_Oless__than @ ( c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Wellfounded_Olex__prod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__less__def) ).
thf(9757,plain,
( c_FunDef_Opair__less
= ( c_Wellfounded_Oless__than @ ( c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Wellfounded_Olex__prod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(2236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( D @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL1) ).
thf(13375,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( D @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2236]) ).
thf(2812,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I12_J) ).
thf(15750,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2812]) ).
thf(3905,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ c_Orderings_Otop__class_Otop ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__unique) ).
thf(20147,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ c_Orderings_Otop__class_Otop ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3905]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
<=> ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
thf(8735,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B ) ) )
=> ( C
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
=> ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(3567,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
thf(18790,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3567]) ).
thf(305,axiom,
tc_HOL_Obool @ class_Lattices_Osemilattice__sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
thf(5816,plain,
tc_HOL_Obool @ class_Lattices_Osemilattice__sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(1035,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olenlex ) )
= ( A @ ( B @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_OPair ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ c_member @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ c_COMBS ) ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fdisj @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ c_COMBS ) ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lenlex__conv) ).
thf(8620,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olenlex ) )
= ( A @ ( B @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_OPair ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ c_member @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ c_COMBS ) ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fdisj @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ c_COMBS ) ) @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(136,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(5202,plain,
tc_Nat_Onat @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(2481,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).
thf(14458,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2481]) ).
thf(3734,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__append) ).
thf(19449,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3734]) ).
thf(906,axiom,
! [A: $i] :
( ( ( A @ c_Int_OBit0 )
= c_Int_OPls )
<=> ( A = c_Int_OPls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
thf(8192,plain,
! [A: $i] :
( ( ( A = c_Int_OPls )
=> ( ( A @ c_Int_OBit0 )
= c_Int_OPls ) )
& ( ( ( A @ c_Int_OBit0 )
= c_Int_OPls )
=> ( A = c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(3118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( E @ c_Set_OCollect @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Set_OCollect @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect__mono) ).
thf(16984,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( E @ c_Set_OCollect @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Set_OCollect @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3118]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I11_J) ).
thf(7768,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Com_Ocom @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(1116,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Orotate ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__id) ).
thf(8958,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Orotate ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(1786,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_prod ) @ c_HOL_OThe ) )
= ( B @ ( C @ c_Product__Type_OPair ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ ( C @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_HOL_OThe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__The) ).
thf(11669,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_prod ) @ c_HOL_OThe ) )
= ( B @ ( C @ c_Product__Type_OPair ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ ( C @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_HOL_OThe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786]) ).
thf(2842,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__equiv__class) ).
thf(15880,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2842]) ).
thf(2412,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff__nat) ).
thf(14122,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2412]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I34_J) ).
thf(5657,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(2264,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert) ).
thf(13499,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2264]) ).
thf(2154,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__UNIV) ).
thf(13050,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2154]) ).
thf(1859,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).
thf(11947,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1859]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Olast ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__upt) ).
thf(5920,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Olast ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(2904,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinsert__remove) ).
thf(16139,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2904]) ).
thf(3708,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__int) ).
thf(19340,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3708]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ c_Relation_OId @ ( A @ ( B @ ( B @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_R__O__Id) ).
thf(7275,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ c_Relation_OId @ ( A @ ( B @ ( B @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(3590,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(18876,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3590]) ).
thf(2373,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) ) )
=> ( ( D @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( A @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class) ).
thf(13930,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) ) )
=> ( ( D @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( A @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2373]) ).
thf(4333,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert) ).
thf(21837,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4333]) ).
thf(2715,axiom,
tc_Int_Oint @ class_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
thf(15389,plain,
tc_Int_Oint @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2715]) ).
thf(1467,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Otl @ hAPP ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I1_J) ).
thf(10375,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Otl @ hAPP ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(4440,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__cancel) ).
thf(22212,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4440]) ).
thf(1355,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).
thf(9888,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil2) ).
thf(5730,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(3991,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
thf(20430,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3991]) ).
thf(893,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__over) ).
thf(8156,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(2460,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( C @ c_Relation_Orefl__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onI) ).
thf(14365,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( C @ c_Relation_Orefl__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2460]) ).
thf(1284,axiom,
tc_Nat_Onat @ class_Rings_Odvd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
thf(9655,plain,
tc_Nat_Onat @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(4790,plain,
! [B: $i,A: $i] :
( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Olinordered__idom ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Olinordered__idom ) ) ),
inference(cnf,[status(esa)],[4789]) ).
thf(4792,plain,
! [B: $i,A: $i] :
( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Olinordered__idom ) ),
inference(cnfConj,[status(thm)],[4790]) ).
thf(40216,plain,
! [B: $i,A: $i] :
( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Olinordered__idom ) ),
inference(rewrite,[status(thm)],[4792,7678]) ).
thf(3325,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
thf(17769,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3325]) ).
thf(3099,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( C @ ( D @ ( A @ ( F @ ( B @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on) ).
thf(16926,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( C @ ( D @ ( A @ ( F @ ( B @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3099]) ).
thf(2743,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( D
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons_H) ).
thf(15497,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( D
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2743]) ).
thf(1428,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(10179,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(3008,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
thf(16570,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3008]) ).
thf(2352,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Onat__set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J) ).
thf(13857,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Onat__set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2352]) ).
thf(349,axiom,
! [A: $i] : ( A @ c_Int_Oint__ge__less__than2 @ ( tc_Int_Oint @ c_Wellfounded_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__int__ge__less__than2) ).
thf(5994,plain,
! [A: $i] : ( A @ c_Int_Oint__ge__less__than2 @ ( tc_Int_Oint @ c_Wellfounded_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(2755,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeast @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc__greaterThan) ).
thf(15543,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeast @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2755]) ).
thf(879,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ c_Nat__Transfer_Otsub ) @ c_Nat__Transfer_Ois__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).
thf(8103,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ c_Nat__Transfer_Otsub ) @ c_Nat__Transfer_Ois__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(3971,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowI) ).
thf(20371,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3971]) ).
thf(55,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Orev @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__rev) ).
thf(4911,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Orev @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(2224,axiom,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Set_OCollect @ hAPP ) @ c_Nat__Transfer_Onat__set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).
thf(13323,plain,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Set_OCollect @ hAPP ) @ c_Nat__Transfer_Onat__set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2224]) ).
thf(1845,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__idem) ).
thf(11893,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1845]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ c_Int_Osucc )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__def) ).
thf(5175,plain,
! [A: $i] :
( ( A @ c_Int_Osucc )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1294,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(9691,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
thf(6989,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(1717,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( C @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
thf(11392,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( C @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717]) ).
thf(4279,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__Suc0__iff) ).
thf(21607,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4279]) ).
thf(3300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( A @ hAPP ) @ hBOOL )
=> ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( A @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__less) ).
thf(17682,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( A @ hAPP ) @ hBOOL )
=> ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( A @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3300]) ).
thf(2034,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(12572,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2034]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Olist_Olist__size ) ) )
= ( A @ ( B @ ( D @ ( C @ ( tc_Nat_Onat @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_Olist_Olist__size ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__map) ).
thf(6800,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Olist_Olist__size ) ) )
= ( A @ ( B @ ( D @ ( C @ ( tc_Nat_Onat @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_Olist_Olist__size ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(4174,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i] :
( ~ ( D @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ? [E: $i] :
( A
= ( E @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__decomp__first) ).
thf(21190,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ~ ( D @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ? [E: $i] :
( A
= ( E @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
=> ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ~ ( D @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ? [E: $i] :
( A
= ( E @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4174]) ).
thf(2211,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(13272,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2211]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Oupto ) @ ( C @ ( D @ ( tc_Int_Oint @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).
thf(6725,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Oupto ) @ ( C @ ( D @ ( tc_Int_Oint @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(6974,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(3869,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__constant) ).
thf(20016,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3869]) ).
thf(3573,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib) ).
thf(18815,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3573]) ).
thf(2693,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_member__rec_I2_J) ).
thf(15297,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2693]) ).
thf(3704,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__asym) ).
thf(19330,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3704]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).
thf(4985,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(4570,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(22693,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4570]) ).
thf(3950,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i] : ( C @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__induct) ).
thf(20298,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i] : ( C @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3950]) ).
thf(2510,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff) ).
thf(14576,plain,
! [A: $i,B: $i] :
( ( ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2510]) ).
thf(3363,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( A @ ( A @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__comp__subset) ).
thf(17914,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( A @ ( A @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3363]) ).
thf(4284,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( E @ ( F @ ( G @ ( H @ ( I @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( C @ ( G @ ( H @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ( ( A @ ( E @ hAPP ) @ ( F @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(21635,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( E @ ( F @ ( G @ ( H @ ( I @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( C @ ( G @ ( H @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ( ( A @ ( E @ hAPP ) @ ( F @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4284]) ).
thf(3533,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__f) ).
thf(18612,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3533]) ).
thf(4398,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ( A
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__is__empty) ).
thf(22074,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4398]) ).
thf(3777,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(19634,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3777]) ).
thf(2470,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ? [D: $i,E: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( E
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( E @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= A )
& ~ ( E @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__eq) ).
thf(14402,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i,E: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( E
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( E @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= A )
& ~ ( E @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
=> ( ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ? [D: $i,E: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( E
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( E @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= A )
& ~ ( E @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2470]) ).
thf(3093,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__sup__le__sup) ).
thf(16905,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3093]) ).
thf(1548,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
!= ( E @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un) ).
thf(10732,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
!= ( E @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548]) ).
thf(850,axiom,
tc_Int_Oint @ class_Groups_Oab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
thf(7978,plain,
tc_Int_Oint @ class_Groups_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(1122,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( A @ ( B @ c_List_Onth @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__nth) ).
thf(8974,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( A @ ( B @ c_List_Onth @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(1581,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ c_Divides_OposDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos) ).
thf(10847,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ c_Divides_OposDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581]) ).
thf(1265,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Olinordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).
thf(9553,plain,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Olinordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(3560,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
thf(18763,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3560]) ).
thf(1199,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
thf(9280,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(6747,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Orotate1 @ hAPP ) )
= ( B @ c_List_Olist_ONil ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).
thf(5392,plain,
! [A: $i,B: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Orotate1 @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ c_List_Orotate1 @ hAPP ) )
= ( B @ c_List_Olist_ONil ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(3122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [H: $i] :
( ( D @ ( H @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G != H )
=> ( ( H @ ( B @ hAPP ) @ ( G @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) )
=> ( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oone__class_Oone @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ ( C @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( F @ c_Groups_Oone__class_Oone @ ( B @ ( F @ c_Groups_Oone__class_Oone @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ ( C @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__UN__disjoint) ).
thf(16999,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [H: $i] :
( ( D @ ( H @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G != H )
=> ( ( H @ ( B @ hAPP ) @ ( G @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) )
=> ( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oone__class_Oone @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ ( C @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( F @ c_Groups_Oone__class_Oone @ ( B @ ( F @ c_Groups_Oone__class_Oone @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ ( C @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3122]) ).
thf(793,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_Oconverse ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(7778,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ c_Relation_Oconverse ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__code__numeral__def) ).
thf(6678,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(3823,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(19802,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3823]) ).
thf(624,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).
thf(7141,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(2622,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( A @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).
thf(15049,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( A @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2622]) ).
thf(3067,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( F @ c_List_Oset @ hAPP ) @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip__leftD) ).
thf(16799,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( F @ c_List_Oset @ hAPP ) @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3067]) ).
thf(3524,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( E @ ( A @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__INT) ).
thf(18580,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( E @ ( A @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3524]) ).
thf(1778,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__diff) ).
thf(11640,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778]) ).
thf(4697,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(23174,plain,
! [A: $i,B: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4697]) ).
thf(3394,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converseI) ).
thf(18057,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3394]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Oremdups ) @ ( A @ ( C @ c_List_Oremove1 ) ) )
= ( B @ ( A @ ( C @ c_List_Oremove1 ) ) @ ( C @ c_List_Oremdups ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__remdups) ).
thf(8782,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Oremdups ) @ ( A @ ( C @ c_List_Oremove1 ) ) )
= ( B @ ( A @ ( C @ c_List_Oremove1 ) ) @ ( C @ c_List_Oremdups ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(3563,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaI) ).
thf(18780,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3563]) ).
thf(4715,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__mult )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oempty) ).
thf(23249,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__mult )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4715]) ).
thf(1575,axiom,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
thf(10825,plain,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1575]) ).
thf(3807,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD2) ).
thf(19753,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3807]) ).
thf(33133,plain,
~ ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ),
inference(rewrite,[status(thm)],[9732,4775]) ).
thf(3806,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ~ ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__iff) ).
thf(19747,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3806]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_Osucc @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__succ) ).
thf(4993,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_Osucc @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(2863,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( A @ ( F @ ( G @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G = F ) ) )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
thf(15968,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( A @ ( F @ ( G @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G = F ) ) )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2863]) ).
thf(1185,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__compl) ).
thf(9228,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(2567,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(14824,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2567]) ).
thf(1892,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__vimage__image__eq) ).
thf(12079,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1892]) ).
thf(3108,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).
thf(16952,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3108]) ).
thf(1383,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oremdups ) @ ( B @ c_List_Oremdups ) )
= ( A @ ( B @ c_List_Oremdups ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__remdups) ).
thf(10004,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oremdups ) @ ( B @ c_List_Oremdups ) )
= ( A @ ( B @ c_List_Oremdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(3802,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__image__vimage__eq) ).
thf(19737,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3802]) ).
thf(1137,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(9030,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(1564,axiom,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(10792,plain,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564]) ).
thf(3898,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Equiv__Relations_Opart__equivp ) )
=> ? [C: $i] : ( A @ ( c_fequal @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_COMBI @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ c_COMBS ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OEx @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__typedef) ).
thf(20122,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Equiv__Relations_Opart__equivp ) )
=> ? [C: $i] : ( A @ ( c_fequal @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_COMBI @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ c_COMBS ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OEx @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3898]) ).
thf(950,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(8340,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(2159,axiom,
~ ( c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I7_J) ).
thf(13068,plain,
~ ( c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2159]) ).
thf(13069,plain,
~ ( c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(polarity_switch,[status(thm)],[13068]) ).
thf(3633,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Opair__less @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI1) ).
thf(19054,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Opair__less @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3633]) ).
thf(972,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Omod__div__equality_H) ).
thf(8413,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(4621,axiom,
tc_HOL_Obool @ class_Enum_Oenum,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).
thf(22880,plain,
tc_HOL_Obool @ class_Enum_Oenum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4621]) ).
thf(1713,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Int_OBit0 )
= ( A @ c_Int_OBit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).
thf(11375,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Int_OBit0 )
= ( A @ c_Int_OBit0 ) ) )
& ( ( ( B @ c_Int_OBit0 )
= ( A @ c_Int_OBit0 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713]) ).
thf(2012,axiom,
! [A: $i,B: $i] :
( ! [C: $i] : ( C @ ( B @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__less__ub) ).
thf(12505,plain,
! [A: $i,B: $i] :
( ! [C: $i] : ( C @ ( B @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2012]) ).
thf(3172,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != B )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
thf(17216,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != B )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3172]) ).
thf(1207,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).
thf(9327,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(2959,axiom,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ~ ~ ( A @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(16366,plain,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2959]) ).
thf(2751,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ( I @ ( J @ hAPP ) @ ( K @ hAPP ) )
= ( F @ ( G @ hAPP ) @ ( H @ hAPP ) ) )
=> ( ( I @ ( J @ ( K @ ( C @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= ( F @ ( G @ ( H @ ( A @ ( D @ ( B @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(15528,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ( I @ ( J @ hAPP ) @ ( K @ hAPP ) )
= ( F @ ( G @ hAPP ) @ ( H @ hAPP ) ) )
=> ( ( I @ ( J @ ( K @ ( C @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= ( F @ ( G @ ( H @ ( A @ ( D @ ( B @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2751]) ).
thf(4212,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__is__subset) ).
thf(21341,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4212]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).
thf(6376,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1612,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(10970,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612]) ).
thf(4550,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
thf(22612,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4550]) ).
thf(1132,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
thf(9018,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(1779,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__all) ).
thf(11643,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779]) ).
thf(3007,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ c_Divides_OposDivAlg ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__0) ).
thf(16567,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ c_Divides_OposDivAlg ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3007]) ).
thf(2862,axiom,
! [A: $i] :
( ? [B: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ? [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).
thf(15960,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ? [B: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2862]) ).
thf(2356,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Relation_Orefl__on ) ) )
=> ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olistrel1 ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__subset__listrel) ).
thf(13867,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Relation_Orefl__on ) ) )
=> ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olistrel1 ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2356]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Enum_On__lists ) ) @ ( C @ tc_List_Olist @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__n__lists) ).
thf(8052,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Enum_On__lists ) ) @ ( C @ tc_List_Olist @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1999,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
thf(12460,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1999]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit1) ).
thf(4832,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1565,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
thf(10793,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565]) ).
thf(3035,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(16670,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3035]) ).
thf(3409,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__add__Un) ).
thf(18121,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3409]) ).
thf(3518,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(18567,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3518]) ).
thf(1705,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(11348,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705]) ).
thf(3237,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le__fold__inf) ).
thf(17444,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3237]) ).
thf(4063,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI1) ).
thf(20682,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4063]) ).
thf(2913,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(16170,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2913]) ).
thf(3299,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__replicate) ).
thf(17679,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3299]) ).
thf(3088,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).
thf(16887,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3088]) ).
thf(3756,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I13_J) ).
thf(19548,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3756]) ).
thf(3853,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
thf(19957,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3853]) ).
thf(1024,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Random_Oselect ) )
= ( c_Code__Numeral_Onat__of @ ( A @ ( B @ c_List_Onth @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ ( B @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ c_Product__Type_OPair ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ c_Random_Orange @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__def) ).
thf(8588,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Random_Oselect ) )
= ( c_Code__Numeral_Onat__of @ ( A @ ( B @ c_List_Onth @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ ( B @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ c_Product__Type_OPair ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ c_Random_Orange @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
thf(5216,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(2888,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(16057,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2888]) ).
thf(1799,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__iff) ).
thf(11711,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1799]) ).
thf(3764,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
thf(19587,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3764]) ).
thf(4085,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I1_J) ).
thf(20805,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4085]) ).
thf(2023,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
thf(12534,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2023]) ).
thf(1688,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Equiv__Relations_Opart__equivp ) )
<=> ( ! [C: $i,D: $i] :
( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) )
& ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ? [C: $i] : ( C @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__def) ).
thf(11262,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i,D: $i] :
( ( ( ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) )
& ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) )
& ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
& ? [C: $i] : ( C @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ c_Equiv__Relations_Opart__equivp ) ) )
& ( ( A @ ( B @ c_Equiv__Relations_Opart__equivp ) )
=> ( ! [C: $i,D: $i] :
( ( ( ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) )
& ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) )
& ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
& ? [C: $i] : ( C @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688]) ).
thf(2988,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__def) ).
thf(16493,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2988]) ).
thf(2090,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).
thf(12779,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2090]) ).
thf(2479,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I9_J) ).
thf(14453,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2479]) ).
thf(4264,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(21545,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4264]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).
thf(8719,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_List_Oupto ) @ ( C @ ( tc_Int_Oint @ c_List_Olist__all ) ) )
<=> ( A @ ( B @ ( C @ c_List_Oall__interval__int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__iff__all__interval__int) ).
thf(7929,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Oall__interval__int ) ) )
=> ( A @ ( B @ c_List_Oupto ) @ ( C @ ( tc_Int_Oint @ c_List_Olist__all ) ) ) )
& ( ( A @ ( B @ c_List_Oupto ) @ ( C @ ( tc_Int_Oint @ c_List_Olist__all ) ) )
=> ( A @ ( B @ ( C @ c_List_Oall__interval__int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1796,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).
thf(11701,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1796]) ).
thf(3957,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Olinordered__ab__semigroup__add )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min__commute) ).
thf(20323,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Olinordered__ab__semigroup__add )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3957]) ).
thf(2846,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
thf(15898,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2846]) ).
thf(3767,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I5_J) ).
thf(19602,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3767]) ).
thf(1084,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( tc_HOL_Obool @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__map) ).
thf(8821,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( tc_HOL_Obool @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(3529,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( C @ ( D @ c_List_Oset @ hAPP ) @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__subset__insert) ).
thf(18602,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( C @ ( D @ c_List_Oset @ hAPP ) @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3529]) ).
thf(1503,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__abs) ).
thf(10514,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503]) ).
thf(4069,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert__iff) ).
thf(20717,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4069]) ).
thf(1510,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Oab__semigroup__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__insert) ).
thf(10544,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Oab__semigroup__mult )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ ( E @ ( F @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510]) ).
thf(3779,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).
thf(19648,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3779]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_OdropWhile ) ) )
= ( A @ ( B @ ( D @ c_List_OdropWhile ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__append2) ).
thf(6738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_OdropWhile ) ) )
= ( A @ ( B @ ( D @ c_List_OdropWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(2199,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(13236,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2199]) ).
thf(1447,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zdiv) ).
thf(10240,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(4395,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty2) ).
thf(22067,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4395]) ).
thf(3288,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( D @ ( B @ ( C @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( A @ ( E @ ( F @ ( B @ ( H @ ( C @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( H @ c_Fun_Obij__betw ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__trans) ).
thf(17647,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( D @ ( B @ ( C @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( A @ ( E @ ( F @ ( B @ ( H @ ( C @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( H @ c_Fun_Obij__betw ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3288]) ).
thf(1376,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) )
= ( A @ ( D @ ( B @ ( C @ c_List_Obutlast ) @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ) )
& ( ( D
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) )
= ( B @ ( C @ c_List_Obutlast ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__list__update) ).
thf(9975,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) )
= ( A @ ( D @ ( B @ ( C @ c_List_Obutlast ) @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ) )
& ( ( D
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) )
= ( B @ ( C @ c_List_Obutlast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(1646,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I5_J) ).
thf(11102,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646]) ).
thf(1339,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( C @ c_Relation_Osingle__valued ) ) )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_Relation_Osingle__valued ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__rel__pow) ).
thf(9841,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( C @ c_Relation_Osingle__valued ) ) )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_Relation_Osingle__valued ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(3654,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(19125,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3654]) ).
thf(2832,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__greaterThan) ).
thf(15849,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2832]) ).
thf(2746,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__distrib) ).
thf(15511,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2746]) ).
thf(4220,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
thf(21365,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4220]) ).
thf(4056,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imp__bij__betw) ).
thf(20660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4056]) ).
thf(2795,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(15689,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2795]) ).
thf(1596,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OposDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__1__number__of) ).
thf(10893,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Divides_OposDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596]) ).
thf(1615,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
thf(10984,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615]) ).
thf(1873,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(12006,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1873]) ).
thf(3669,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).
thf(19179,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3669]) ).
thf(45162,plain,
! [A: $i] :
( ( ( A @ ( v_c @ ( c_Int_OPls @ hAPP ) @ hAPP ) )
!= ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(paramod_ordered,[status(thm)],[8226,39006]) ).
thf(45624,plain,
! [A: $i] :
( ( A != c_Int_OPls )
| ( ( v_c @ ( c_Int_OPls @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[45162]) ).
thf(45730,plain,
( ( ( v_c @ ( c_Int_OPls @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
| ( ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[45624]) ).
thf(4372,axiom,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold1SetE) ).
thf(21982,plain,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4372]) ).
thf(2720,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( C @ c_List_Olexn ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lexn) ).
thf(15405,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( C @ c_List_Olexn ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2720]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
=> ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__lengthD) ).
thf(5042,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
=> ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(4118,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
thf(20961,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4118]) ).
thf(1365,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ! [C: $i] :
( ( A @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__eq__0__conv) ).
thf(9916,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( A @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ! [C: $i] :
( ( A @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(4382,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I3_J) ).
thf(22021,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4382]) ).
thf(4670,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__empty) ).
thf(23062,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4670]) ).
thf(1976,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ hBOOL ) )
<=> ( B @ ( A @ ( C @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ball__set__list__all) ).
thf(12373,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ c_List_Olist__all ) ) )
=> ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( C @ c_List_Olist__all ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1976]) ).
thf(3742,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infE) ).
thf(19499,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3742]) ).
thf(3913,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__iff) ).
thf(20176,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Set_OPow @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3913]) ).
thf(3902,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).
thf(20132,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3902]) ).
thf(1475,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I1_J) ).
thf(10407,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).
thf(1766,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
thf(11607,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766]) ).
thf(2008,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__asym) ).
thf(12497,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2008]) ).
thf(1154,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( B @ tc_List_Olist @ c_List_Olist_ONil ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ! [D: $i] :
( ( C @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( B @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= A ) )
=> ( ( C @ ( B @ c_List_Otranspose ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( C @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( C @ ( B @ tc_List_Olist @ c_List_Onth @ hAPP ) @ ( B @ c_List_Onth @ ( tc_Nat_Onat @ ( B @ ( tc_Nat_Onat @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_List_Omap ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ tc_List_Olist @ tc_fun ) @ ( B @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ tc_List_Olist @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__rectangle) ).
thf(9106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( B @ tc_List_Olist @ c_List_Olist_ONil ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ! [D: $i] :
( ( C @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( B @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= A ) )
=> ( ( C @ ( B @ c_List_Otranspose ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( C @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( C @ ( B @ tc_List_Olist @ c_List_Onth @ hAPP ) @ ( B @ c_List_Onth @ ( tc_Nat_Onat @ ( B @ ( tc_Nat_Onat @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_List_Omap ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ tc_List_Olist @ tc_fun ) @ ( B @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ tc_List_Olist @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(3147,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ ( D @ ( B @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( B @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__inv__o__cancel) ).
thf(17102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ ( D @ ( B @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( B @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3147]) ).
thf(4169,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__reflclI) ).
thf(21166,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4169]) ).
thf(2766,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( c_fequal @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( D @ c_Relation_OId @ ( C @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__set__eq) ).
thf(15583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ c_Relation_OId @ ( C @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_fequal @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( c_fequal @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ c_Relation_OId @ ( C @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2766]) ).
thf(39021,plain,
! [A: $i] :
( ( ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(rewrite,[status(thm)],[23986,7678]) ).
thf(3370,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__Int) ).
thf(17940,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3370]) ).
thf(2285,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).
thf(13598,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2285]) ).
thf(1765,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__take) ).
thf(11605,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).
thf(1350,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(9871,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(315,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Oconcat ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat_Osimps_I1_J) ).
thf(5849,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Oconcat ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(4503,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( B @ hAPP ) @ hBOOL ) )
=> ( C @ ( D @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).
thf(22427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( B @ hAPP ) @ hBOOL ) )
=> ( C @ ( D @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4503]) ).
thf(1602,axiom,
! [A: $i] :
( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2) ).
thf(10930,plain,
! [A: $i] :
( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( D @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( B @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) )
=> ( B @ ( D @ ( C @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__obtain__same__length) ).
thf(5725,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( D @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( B @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) )
=> ( B @ ( D @ ( C @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(1481,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(10424,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(4294,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(21671,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4294]) ).
thf(4335,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(21842,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4335]) ).
thf(3908,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(20154,plain,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3908]) ).
thf(1213,axiom,
( c_Code__Numeral_Oof__nat
= ( tc_Code__Numeral_Ocode__numeral @ c_Nat_Osemiring__1__class_Oof__nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).
thf(9345,plain,
( c_Code__Numeral_Oof__nat
= ( tc_Code__Numeral_Ocode__numeral @ c_Nat_Osemiring__1__class_Oof__nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(3787,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) )
<=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).
thf(19680,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3787]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Osplice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice__Nil2) ).
thf(5817,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(1703,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit0) ).
thf(11342,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703]) ).
thf(1138,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__nat__number__of) ).
thf(9033,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(4041,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
thf(20607,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4041]) ).
thf(688,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(7366,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rotate1) ).
thf(5667,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(1922,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ~ ( E @ ( A @ hAPP ) @ ( A @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole__infinite) ).
thf(12178,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ~ ( E @ ( A @ hAPP ) @ ( A @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1922]) ).
thf(2871,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
thf(15992,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2871]) ).
thf(4359,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_List_Olist_ONil @ ( A @ c_List_Olistset ) )
= ( tc_HOL_Obool @ ( A @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_List_Olist_ONil @ ( A @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listset_Osimps_I1_J) ).
thf(21938,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_List_Olist_ONil @ ( A @ c_List_Olistset ) )
= ( tc_HOL_Obool @ ( A @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_List_Olist_ONil @ ( A @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4359]) ).
thf(3502,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).
thf(18505,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3502]) ).
thf(1933,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(12224,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1933]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).
thf(6027,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(2585,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastLessThan__int) ).
thf(14877,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2585]) ).
thf(1653,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ c_List_Olist_ONil )
= ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).
thf(11141,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) )
=> ( ( C @ c_List_Olist_ONil )
= ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ c_List_Olist_ONil )
= ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653]) ).
thf(4400,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( C @ ( A @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( B @ ( A @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut) ).
thf(22084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( C @ ( A @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( B @ ( A @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4400]) ).
thf(1309,axiom,
! [A: $i,B: $i] :
( ( B @ ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).
thf(9740,plain,
! [A: $i,B: $i] :
( ( B @ ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(1414,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ c_Nat__Transfer_Ois__nat ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( c_Int_Onat @ ( C @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).
thf(10119,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ c_Nat__Transfer_Ois__nat ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( c_Int_Onat @ ( C @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).
thf(2976,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Relation_Oconverse ) @ ( C @ ( tc_HOL_Obool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__UNION) ).
thf(16435,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Relation_Oconverse ) @ ( C @ ( tc_HOL_Obool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2976]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power3__eq__cube) ).
thf(5089,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1741,axiom,
c_fTrue @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ c_COMBK ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Nat__Transfer_Otransfer__morphism ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__morphism__int__nat) ).
thf(11507,plain,
c_fTrue @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ c_COMBK ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Nat__Transfer_Otransfer__morphism ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741]) ).
thf(2925,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Inter) ).
thf(16217,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2925]) ).
thf(4326,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Opair__leq @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leqI2) ).
thf(21814,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Opair__leq @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4326]) ).
thf(684,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Ois__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).
thf(7356,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( ( A @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Ois__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(2604,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Ofst ) @ ( C @ ( B @ ( C @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__eq__Domain) ).
thf(14947,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Ofst ) @ ( C @ ( B @ ( C @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2604]) ).
thf(4131,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(21019,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4131]) ).
thf(1163,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__minus1__right) ).
thf(9150,plain,
! [A: $i] :
( ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(1067,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I2_J) ).
thf(8763,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(2316,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [B: $i] :
( A
!= ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__cases) ).
thf(13727,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [B: $i] :
( A
!= ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2316]) ).
thf(4423,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Wellfounded_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__empty) ).
thf(22152,plain,
! [A: $i] : ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Wellfounded_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4423]) ).
thf(3358,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__mono) ).
thf(17896,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3358]) ).
thf(1014,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) )
= ( A @ ( C @ c_List_Obutlast ) @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__drop) ).
thf(8560,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) )
= ( A @ ( C @ c_List_Obutlast ) @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(2029,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
thf(12557,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2029]) ).
thf(1709,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__semigroup__mult )
=> ( A @ c_Groups_Otimes__class_Otimes @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm) ).
thf(11359,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__semigroup__mult )
=> ( A @ c_Groups_Otimes__class_Otimes @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709]) ).
thf(4030,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Relation_OField @ hAPP ) )
= ( A @ ( B @ c_Relation_OField @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Union) ).
thf(20564,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Relation_OField @ hAPP ) )
= ( A @ ( B @ c_Relation_OField @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4030]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) @ ( B @ c_List_Olinorder__class_Osorted ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__sort) ).
thf(4965,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) @ ( B @ c_List_Olinorder__class_Osorted ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(2529,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I1_J) ).
thf(14650,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2529]) ).
thf(3725,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Wellfounded_Omax__extp ) ) ) )
<=> ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).
thf(19409,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Wellfounded_Omax__extp ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Wellfounded_Omax__extp ) ) ) )
=> ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3725]) ).
thf(1710,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__nat__number__of) ).
thf(11361,plain,
! [A: $i,B: $i] :
( ( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710]) ).
thf(4103,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
thf(20907,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4103]) ).
thf(2946,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I7_J) ).
thf(16305,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2946]) ).
thf(1318,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( B @ c_List_Olist_ONil @ ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc__conv__app__nth) ).
thf(9762,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( B @ c_List_Olist_ONil @ ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(3333,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I10_J) ).
thf(17809,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3333]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).
thf(6730,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(2514,axiom,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).
thf(14599,plain,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2514]) ).
thf(2362,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__supI1) ).
thf(13889,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2362]) ).
thf(4090,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).
thf(20828,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4090]) ).
thf(2753,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).
thf(15534,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2753]) ).
thf(3293,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I17_J) ).
thf(17664,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3293]) ).
thf(3967,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__memI) ).
thf(20351,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3967]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(7154,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(1929,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
<=> ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
thf(12207,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) ) )
=> ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) )
& ( ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1929]) ).
thf(4654,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__0) ).
thf(23016,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4654]) ).
thf(2272,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
thf(13528,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2272]) ).
thf(2894,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_O__assoc) ).
thf(16094,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2894]) ).
thf(2119,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I8_J) ).
thf(12886,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2119]) ).
thf(1372,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) )
=> ( ( B @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Otranspose ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ ( C @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__column__length) ).
thf(9958,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) )
=> ( ( B @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Otranspose ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ ( C @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).
thf(5661,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(3229,axiom,
! [A: $i,B: $i] : ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Relation_Orefl__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__reflcl) ).
thf(17413,plain,
! [A: $i,B: $i] : ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Relation_Orefl__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3229]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last_Osimps) ).
thf(6768,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(657,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ c_List_Odrop @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons) ).
thf(7260,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ c_List_Odrop @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(3117,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I46_J) ).
thf(16980,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3117]) ).
thf(3281,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
thf(17625,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3281]) ).
thf(2492,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( F @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( G @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__mono) ).
thf(14493,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( F @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( G @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2492]) ).
thf(4209,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__pos) ).
thf(21329,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4209]) ).
thf(1504,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Oadjust @ hAPP ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_adjust__eq) ).
thf(10517,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Oadjust @ hAPP ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(4081,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__sup__iff) ).
thf(20783,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4081]) ).
thf(1152,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( c_Int_Onat @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__number__of__Suc) ).
thf(9097,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( c_Int_Onat @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat__Numeral_Oneg @ ( tc_Nat_Onat @ c_If @ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(4351,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__iff) ).
thf(21901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4351]) ).
thf(2821,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(15804,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2821]) ).
thf(4647,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib2) ).
thf(22984,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4647]) ).
thf(2158,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( C @ ( B @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( C @ c_Fun_Oid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__o__cancel) ).
thf(13065,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( C @ ( B @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( C @ c_Fun_Oid ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2158]) ).
thf(1697,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_Oinsert ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__insert) ).
thf(11316,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_Oinsert ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697]) ).
thf(2906,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
thf(16143,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2906]) ).
thf(229,axiom,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0) ).
thf(5538,plain,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(4377,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).
thf(22005,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4377]) ).
thf(3120,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omax @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).
thf(16991,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omax @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3120]) ).
thf(2234,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Osublist ) ) @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sublist__subset) ).
thf(13371,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Osublist ) ) @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2234]) ).
thf(2589,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
<=> ( ( A @ ( C @ c_Relation_Otrans ) )
& ( A @ ( C @ c_Relation_Osym ) )
& ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__def) ).
thf(14887,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ c_Relation_Otrans ) )
& ( A @ ( C @ c_Relation_Osym ) )
& ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) ) )
=> ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) ) )
& ( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( A @ ( C @ c_Relation_Otrans ) )
& ( A @ ( C @ c_Relation_Osym ) )
& ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2589]) ).
thf(1450,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(10322,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(3694,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Product__Type_OPair ) @ ( B @ ( C @ tc_prod ) @ ( B @ ( C @ c_COMBC ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( B @ ( C @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__def) ).
thf(19293,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Product__Type_OPair ) @ ( B @ ( C @ tc_prod ) @ ( B @ ( C @ c_COMBC ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( B @ ( C @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3694]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__eq__iff__index__eq) ).
thf(9170,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(4482,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Big__Operators_Olinorder__class_OMax ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Osingleton) ).
thf(22359,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Big__Operators_Olinorder__class_OMax ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4482]) ).
thf(714,axiom,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_COMBI @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Bit1) ).
thf(7490,plain,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_COMBI @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(2719,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ hAPP ) @ hBOOL ) ) )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__induct__0) ).
thf(15400,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ hAPP ) @ hBOOL ) ) )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2719]) ).
thf(4100,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(20896,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4100]) ).
thf(3754,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I16_J) ).
thf(19542,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3754]) ).
thf(576,axiom,
tc_Nat_Onat @ class_Groups_Olinordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).
thf(6977,plain,
tc_Nat_Onat @ class_Groups_Olinordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(2716,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(15390,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2716]) ).
thf(2066,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I3_J) ).
thf(12708,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2066]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ ( D @ c_List_Olist__all2 ) ) ) ) )
<=> ( A
= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__Nil2) ).
thf(4901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( D @ c_List_Olist_ONil ) )
=> ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ ( D @ c_List_Olist__all2 ) ) ) ) ) )
& ( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ ( D @ c_List_Olist__all2 ) ) ) ) )
=> ( A
= ( D @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1879,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ? [E: $i] :
( ( E @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__SucD) ).
thf(12021,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ? [E: $i] :
( ( E @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1879]) ).
thf(3139,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
thf(17070,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3139]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__drop) ).
thf(6417,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(2608,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( D @ ( E @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( E @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__disj) ).
thf(14966,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( D @ ( E @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( E @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2608]) ).
thf(3963,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(20338,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3963]) ).
thf(1288,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__Suc) ).
thf(9673,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(2685,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__eq__Inter__image) ).
thf(15276,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2685]) ).
thf(3791,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
thf(19695,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3791]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus) ).
thf(5881,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(1635,axiom,
( c_FunDef_Omax__weak
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_FunDef_Opair__leq @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Omax__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__weak__def) ).
thf(11062,plain,
( c_FunDef_Omax__weak
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_FunDef_Opair__leq @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Omax__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635]) ).
thf(4136,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__lessThan__Suc) ).
thf(21031,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4136]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__addf) ).
thf(7296,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(2354,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__disjoint) ).
thf(13861,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2354]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__add) ).
thf(4868,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(3988,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold1__belowI) ).
thf(20423,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3988]) ).
thf(3722,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterI) ).
thf(19399,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3722]) ).
thf(3220,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_List_Oset @ hAPP ) @ ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__mem) ).
thf(17383,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_List_Oset @ hAPP ) @ ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3220]) ).
thf(698,axiom,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(7403,plain,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(1431,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_List_Oupt ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_List_Oupt ) @ ( B @ ( C @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__add__eq__append) ).
thf(10191,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_List_Oupt ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_List_Oupt ) @ ( B @ ( C @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(849,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__code__numeral__def) ).
thf(7975,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(4151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__commute) ).
thf(21097,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4151]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(7371,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(1522,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OposDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OposDivAlg ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Divides_OposDivAlg ) @ ( A @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OposDivAlg ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Opsimps) ).
thf(10589,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Divides_OposDivAlg__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OposDivAlg ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Divides_OposDivAlg ) @ ( A @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OposDivAlg ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).
thf(3009,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I7_J) ).
thf(16574,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3009]) ).
thf(3813,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI1) ).
thf(19770,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3813]) ).
thf(4285,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__subset) ).
thf(21639,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4285]) ).
thf(1268,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).
thf(9563,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(4132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__lower) ).
thf(21022,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4132]) ).
thf(2437,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(14250,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2437]) ).
thf(4052,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( A @ c_Orderings_Oord__class_Omax @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).
thf(20650,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( A @ c_Orderings_Oord__class_Omax @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4052]) ).
thf(3097,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplD) ).
thf(16922,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3097]) ).
thf(2640,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__semigroup__mult )
=> ( ( B @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__permute__diff) ).
thf(15112,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__semigroup__mult )
=> ( ( B @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2640]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(8099,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(4346,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__distrib1) ).
thf(21878,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4346]) ).
thf(2892,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UN) ).
thf(16089,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2892]) ).
thf(1408,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(10091,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( D @ ( C @ ( E @ c_List_Onth @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__via__drop) ).
thf(6659,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( D @ ( C @ ( E @ c_List_Onth @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(4451,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Big__Operators_Olattice__class_OInf__fin ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Osingleton) ).
thf(22251,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Big__Operators_Olattice__class_OInf__fin ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4451]) ).
thf(4409,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__quotient) ).
thf(22110,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4409]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__commute) ).
thf(6088,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(2408,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olistrel1 ) @ ( B @ ( C @ c_List_Olistrel1 ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__mono) ).
thf(14106,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olistrel1 ) @ ( B @ ( C @ c_List_Olistrel1 ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2408]) ).
thf(395,axiom,
! [A: $i] :
( ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__inverse) ).
thf(6191,plain,
! [A: $i] :
( ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(2851,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_OwfP ) )
<=> ! [C: $i] : ( C @ ( A @ ( B @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
thf(15918,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( C @ ( A @ ( B @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_OwfP ) ) )
& ( ( A @ ( B @ c_Wellfounded_OwfP ) )
=> ! [C: $i] : ( C @ ( A @ ( B @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2851]) ).
thf(1487,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ c_Divides_Odivmod__nat ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__nat__def) ).
thf(10449,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ c_Divides_Odivmod__nat ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_Osnd ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).
thf(4230,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__set__diff) ).
thf(21405,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4230]) ).
thf(2884,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__eq__subset__Compl) ).
thf(16042,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2884]) ).
thf(4879,plain,
( ( c_Int_OMin @ c_Int_Osucc )
= c_Int_OPls ),
inference(lifteq,[status(thm)],[4878]) ).
thf(1113,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__odd__eq) ).
thf(8949,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(999,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Ono__zero__divisors )
& ( D @ class_Rings_Ocomm__semiring__1 ) )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
<=> ? [E: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
& ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__zero__iff) ).
thf(8505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Ono__zero__divisors )
& ( D @ class_Rings_Ocomm__semiring__1 ) )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ? [E: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
& ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ? [E: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
& ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(1228,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_HOL_OThe ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).
thf(9408,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_HOL_OThe ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(3339,axiom,
! [A: $i] :
( ( A @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__empty) ).
thf(17826,plain,
! [A: $i] :
( ( A @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3339]) ).
thf(1939,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Groups_Ocomm__monoid__mult )
& ( C @ class_Groups_Ocomm__monoid__add ) )
=> ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( c_Int_Onat @ ( B @ ( tc_Int_Oint @ ( C @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I1_J) ).
thf(12239,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Groups_Ocomm__monoid__mult )
& ( C @ class_Groups_Ocomm__monoid__add ) )
=> ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( c_Int_Onat @ ( B @ ( tc_Int_Oint @ ( C @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1939]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( D @ ( B @ ( F @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( G @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ ( G @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__update) ).
thf(8323,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( D @ ( B @ ( F @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( G @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ ( G @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(1570,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__2) ).
thf(10814,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570]) ).
thf(1089,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Divides_Odivmod__nat ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__step) ).
thf(8836,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Divides_Odivmod__nat ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(2652,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).
thf(15152,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2652]) ).
thf(638,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Ohd @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd_Osimps) ).
thf(7190,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Ohd @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(3601,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( D @ ( A @ hAPP ) @ ( E @ ( A @ hAPP ) @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__inv__image) ).
thf(18913,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( D @ ( A @ hAPP ) @ ( E @ ( A @ hAPP ) @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( F @ ( C @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( F @ ( C @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP ) @ ( E @ ( A @ hAPP ) @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3601]) ).
thf(1280,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Odistinct @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__upt) ).
thf(9639,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Odistinct @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(1901,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup__absorb) ).
thf(12107,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1901]) ).
thf(1290,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( B @ ( A @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( E @ ( D @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__inv__into) ).
thf(9678,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( B @ ( A @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( E @ ( D @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__even) ).
thf(5678,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(1285,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(9656,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(124,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).
thf(5165,plain,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(3952,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty) ).
thf(20302,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3952]) ).
thf(4216,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ ( B @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__bij__betw__finite__nat) ).
thf(21350,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ ( B @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4216]) ).
thf(1991,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(12434,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1991]) ).
thf(1954,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__lessThan) ).
thf(12294,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1954]) ).
thf(1792,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
thf(11689,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1792]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__nth) ).
thf(7679,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Osublist ) ) )
= ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( B @ ( D @ c_List_Osublist ) ) @ ( A @ ( C @ ( D @ c_List_Osublist ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__append) ).
thf(6076,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Osublist ) ) )
= ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( B @ ( D @ c_List_Osublist ) ) @ ( A @ ( C @ ( D @ c_List_Osublist ) ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(1760,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Relation_Oantisym ) )
<=> ( A @ ( B @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__converse) ).
thf(11579,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Relation_Oantisym ) )
=> ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Relation_Oantisym ) ) )
& ( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Relation_Oantisym ) )
=> ( A @ ( B @ c_Relation_Oantisym ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760]) ).
thf(1046,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose__rel @ ( D @ tc_List_Olist @ tc_List_Olist @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose ) )
= ( A @ ( D @ tc_List_Olist @ c_List_Olist_ONil @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_ONil @ ( D @ ( D @ tc_List_Olist @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Oconcat ) @ ( B @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose ) @ ( A @ ( D @ c_List_Olist_ONil @ ( D @ c_List_Olist_OCons @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_COMBK ) @ ( D @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist_ONil @ ( D @ ( D @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oconcat ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I3_J) ).
thf(8657,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose__rel @ ( D @ tc_List_Olist @ tc_List_Olist @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose ) )
= ( A @ ( D @ tc_List_Olist @ c_List_Olist_ONil @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_ONil @ ( D @ ( D @ tc_List_Olist @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Oconcat ) @ ( B @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose ) @ ( A @ ( D @ c_List_Olist_ONil @ ( D @ c_List_Olist_OCons @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_COMBK ) @ ( D @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist_ONil @ ( D @ ( D @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oconcat ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(4622,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( tc_HOL_Obool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( tc_HOL_Obool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( D @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conseq2) ).
thf(22881,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( tc_HOL_Obool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( tc_HOL_Obool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( D @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4622]) ).
thf(4566,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff) ).
thf(22676,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4566]) ).
thf(617,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).
thf(7120,plain,
c_Int_OMin != c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(7121,plain,
c_Int_OMin != c_Int_OPls,
inference(polarity_switch,[status(thm)],[7120]) ).
thf(7122,plain,
c_Int_OPls != c_Int_OMin,
inference(lifteq,[status(thm)],[7121]) ).
thf(1041,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_COMBI @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__odd) ).
thf(8637,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_COMBI @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(2895,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Oreplicate ) ) )
= ( A @ ( B @ ( C @ c_List_Oreplicate ) ) @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__Suc) ).
thf(16097,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Oreplicate ) ) )
= ( A @ ( B @ ( C @ c_List_Oreplicate ) ) @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2895]) ).
thf(3316,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
<=> ( ( A @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( C @ ( B @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( C @ c_Fun_Oid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__iff) ).
thf(17736,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( C @ ( B @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( C @ c_Fun_Oid ) )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) )
& ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( C @ ( B @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( C @ c_Fun_Oid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3316]) ).
thf(4675,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( H @ ( I @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [J: $i] :
( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( J @ ( C @ hAPP ) @ ( J @ ( D @ hAPP ) @ ( J @ ( E @ hAPP ) @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( J @ ( A @ hAPP ) @ ( J @ ( D @ hAPP ) @ ( J @ ( B @ hAPP ) @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) )
=> ( ( H @ ( C @ ( D @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ ( I @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( I @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ ( I @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( I @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( H @ ( A @ ( D @ ( B @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ ( I @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( I @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ ( I @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( I @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__pointwise) ).
thf(23087,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( H @ ( I @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [J: $i] :
( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( J @ ( C @ hAPP ) @ ( J @ ( D @ hAPP ) @ ( J @ ( E @ hAPP ) @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( J @ ( A @ hAPP ) @ ( J @ ( D @ hAPP ) @ ( J @ ( B @ hAPP ) @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) )
=> ( ( H @ ( C @ ( D @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ ( I @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( I @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ ( I @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( I @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( H @ ( A @ ( D @ ( B @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ ( I @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( I @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( tc_HOL_Obool @ ( tc_Com_Ostate @ tc_fun ) @ ( G @ tc_fun ) @ ( I @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ ( I @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4675]) ).
thf(26685,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4741,25763]) ).
thf(26726,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[26685]) ).
thf(26733,plain,
! [A: $i] :
( ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( A @ class_Rings_Oring__1 ) ),
inference(simp,[status(thm)],[26726]) ).
thf(3670,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).
thf(19182,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3670]) ).
thf(4110,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__dropD) ).
thf(20936,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4110]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).
thf(5710,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1252,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( B @ c_List_Otranspose ) @ ( B @ c_List_Otranspose ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_OtakeWhile ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__transpose) ).
thf(9507,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( B @ c_List_Otranspose ) @ ( B @ c_List_Otranspose ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_List_OtakeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(2214,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Olinordered__ab__semigroup__add )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Max__commute) ).
thf(13292,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Olinordered__ab__semigroup__add )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2214]) ).
thf(4259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__eq) ).
thf(21532,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OEx @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4259]) ).
thf(1455,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__self__div__2) ).
thf(10339,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(2625,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(15058,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2625]) ).
thf(2435,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( C @ ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( G @ tc_fun ) @ ( H @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__D) ).
thf(14240,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( C @ ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( G @ tc_fun ) @ ( H @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2435]) ).
thf(1716,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(11391,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716]) ).
thf(3599,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
thf(18908,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3599]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__mono) ).
thf(6440,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1821,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0__less__iff) ).
thf(11795,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1821]) ).
thf(991,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Wellfounded_Oacyclic ) )
<=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__converse) ).
thf(8477,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Wellfounded_Oacyclic ) ) )
& ( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add) ).
thf(8020,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(499,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(6664,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Rings_Osemiring__1 )
& ( E @ class_Groups_Oordered__ab__semigroup__add ) )
=> ( ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( E @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__bounded) ).
thf(6115,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Rings_Osemiring__1 )
& ( E @ class_Groups_Oordered__ab__semigroup__add ) )
=> ( ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( E @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(4640,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__empty2) ).
thf(22964,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4640]) ).
thf(1491,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Equiv__Relations_Oequivp ) )
=> ( A @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__reflp) ).
thf(10471,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Equiv__Relations_Oequivp ) )
=> ( A @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).
thf(3917,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I3_J) ).
thf(20196,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3917]) ).
thf(3322,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__lessThan) ).
thf(17762,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3322]) ).
thf(1386,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Osnd ) @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Ofst ) @ ( D @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Osnd ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Ofst ) @ ( D @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__shift__lemma) ).
thf(10016,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Osnd ) @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Ofst ) @ ( D @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Osnd ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Product__Type_Ofst ) @ ( D @ ( tc_Nat_Onat @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__number__of) ).
thf(4812,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(2102,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
thf(12817,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2102]) ).
thf(3682,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Un__distrib1) ).
thf(19228,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3682]) ).
thf(3124,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
thf(17019,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3124]) ).
thf(3890,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__eq) ).
thf(20089,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3890]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(6202,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__decreasing) ).
thf(6875,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__add) ).
thf(5414,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(4461,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint) ).
thf(22285,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4461]) ).
thf(2601,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I8_J) ).
thf(14934,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2601]) ).
thf(4637,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_New__DSequence_Opos__empty @ hAPP ) )
= ( B @ c_Lazy__Sequence_Oempty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
thf(22949,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_New__DSequence_Opos__empty @ hAPP ) )
= ( B @ c_Lazy__Sequence_Oempty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4637]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Groups_Oordered__ab__semigroup__add )
& ( E @ class_Groups_Omonoid__add ) )
=> ( ! [F: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__mono) ).
thf(7283,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Groups_Oordered__ab__semigroup__add )
& ( E @ class_Groups_Omonoid__add ) )
=> ( ! [F: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Olinordered__idom )
& ( C @ class_Int_Onumber__ring ) )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of) ).
thf(5446,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Olinordered__idom )
& ( C @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(4665,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I14_J) ).
thf(23052,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4665]) ).
thf(2993,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( c_FunDef_Omax__strict @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__emptyI) ).
thf(16521,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( c_FunDef_Omax__strict @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2993]) ).
thf(2840,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__lesseq) ).
thf(15871,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2840]) ).
thf(1277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).
thf(9631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(1100,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
thf(8905,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(866,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__number__of__eq) ).
thf(8056,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(3816,axiom,
! [A: $i] :
( ( A @ class_Lattices_Oboolean__algebra )
=> ( ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__bot__eq) ).
thf(19778,plain,
! [A: $i] :
( ( A @ class_Lattices_Oboolean__algebra )
=> ( ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3816]) ).
thf(2442,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Oinject) ).
thf(14282,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2442]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp_Oequations_I2_J) ).
thf(6069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(3727,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_List_Orotate ) )
= ( A @ tc_List_Olist @ c_Fun_Oid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate0) ).
thf(19429,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_List_Orotate ) )
= ( A @ tc_List_Olist @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3727]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(7026,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(2610,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).
thf(14972,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ) )
& ( ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2610]) ).
thf(3665,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__into) ).
thf(19167,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3665]) ).
thf(1947,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) )
= ( A @ ( D @ c_List_Oset @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__insort) ).
thf(12266,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) )
= ( A @ ( D @ c_List_Oset @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1947]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_List_Olexn ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Olexn ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ ( C @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ c_List_Olist_OCons @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ c_List_Olist_OCons @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ tc_prod ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ tc_prod ) @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ tc_List_Olist @ ( C @ tc_prod ) @ ( C @ tc_List_Olist @ ( C @ tc_prod ) @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn_Osimps_I2_J) ).
thf(5716,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_List_Olexn ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Olexn ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ ( C @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ c_List_Olist_OCons @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ c_List_Olist_OCons @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ tc_prod ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ tc_prod ) @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ tc_List_Olist @ ( C @ tc_prod ) @ ( C @ tc_List_Olist @ ( C @ tc_prod ) @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(4164,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
thf(21147,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4164]) ).
thf(3171,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Oordered__ab__group__add )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( C @ hAPP ) @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( D @ ( C @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= B )
=> ( ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__nonneg__leq__bound) ).
thf(17208,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Oordered__ab__group__add )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( C @ hAPP ) @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( D @ ( C @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= B )
=> ( ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3171]) ).
thf(1017,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I1_J) ).
thf(8569,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(2061,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(12684,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2061]) ).
thf(2344,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).
thf(13828,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2344]) ).
thf(3269,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(17564,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3269]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__append) ).
thf(6249,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(2109,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__subset) ).
thf(12839,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2109]) ).
thf(4543,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty1) ).
thf(22587,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4543]) ).
thf(3056,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ c_List_Oset @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( E @ c_List_Olist_Olist__size ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__estimation_H) ).
thf(16759,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ c_List_Oset @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( E @ c_List_Olist_Olist__size ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3056]) ).
thf(632,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).
thf(7166,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(4419,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_Orefl__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__empty) ).
thf(22142,plain,
! [A: $i] : ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_Orefl__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4419]) ).
thf(4680,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__empty) ).
thf(23106,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4680]) ).
thf(2738,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(15479,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2738]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
thf(6472,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A )
=> ( ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_OPair ) @ hAPP ) @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_Random_Opick ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick__same) ).
thf(6453,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_OPair ) @ hAPP ) @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ c_Random_Opick ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(1164,axiom,
tc_Int_Oint @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(9153,plain,
tc_Int_Oint @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(2848,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
thf(15905,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2848]) ).
thf(952,axiom,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistsp ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp_ONil) ).
thf(8345,plain,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistsp ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(4692,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(23136,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4692]) ).
thf(1191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( B @ ( D @ ( E @ ( F @ c_List_Ofoldr ) ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_List_Ofoldr ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__append) ).
thf(9253,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( B @ ( D @ ( E @ ( F @ c_List_Ofoldr ) ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_List_Ofoldr ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(1758,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Osym ) )
=> ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__trancl) ).
thf(11575,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Osym ) )
=> ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( B @ ( D @ ( E @ ( F @ c_List_Ofoldr ) ) ) ) @ ( C @ ( D @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr_Osimps_I2_J) ).
thf(6399,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( B @ ( D @ ( E @ ( F @ c_List_Ofoldr ) ) ) ) @ ( C @ ( D @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(602,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__nat__number__of) ).
thf(7058,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1382,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( C @ ( E @ c_Predicate_Opred__comp ) ) ) ) @ ( D @ ( E @ c_Predicate_Oconversep ) ) )
= ( B @ ( C @ ( E @ c_Predicate_Oconversep ) ) @ ( A @ ( D @ ( C @ c_Predicate_Oconversep ) ) @ ( E @ ( C @ ( D @ c_Predicate_Opred__comp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__pred__comp) ).
thf(10001,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( C @ ( E @ c_Predicate_Opred__comp ) ) ) ) @ ( D @ ( E @ c_Predicate_Oconversep ) ) )
= ( B @ ( C @ ( E @ c_Predicate_Oconversep ) ) @ ( A @ ( D @ ( C @ c_Predicate_Oconversep ) ) @ ( E @ ( C @ ( D @ c_Predicate_Opred__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(1732,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) @ ( D @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) @ ( F @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conjI__realizer) ).
thf(11460,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) @ ( D @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) @ ( F @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732]) ).
thf(1159,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__def) ).
thf(9138,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(1757,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).
thf(11573,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757]) ).
thf(2945,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_fdisj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__disjI) ).
thf(16298,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( c_fdisj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( c_fdisj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2945]) ).
thf(1895,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__apply) ).
thf(12088,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1895]) ).
thf(2183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( C @ ( D @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
thf(13181,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( C @ ( D @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2183]) ).
thf(4087,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ ( G @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ ( H @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ ( H @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ tc_fun ) @ ( H @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( H @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( G @ ( H @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( H @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Times__distrib) ).
thf(20811,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ ( G @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) @ ( H @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ ( H @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( G @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( G @ tc_fun ) @ ( H @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( H @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( G @ ( H @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( H @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4087]) ).
thf(2261,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__mono) ).
thf(13491,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2261]) ).
thf(3173,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Sup__fold__sup) ).
thf(17219,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3173]) ).
thf(1768,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Oone__class_Oone @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
thf(11611,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Oone__class_Oone @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( D @ ( C @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__apsnd) ).
thf(5125,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( D @ ( C @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(3644,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( F @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( D @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( F @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__commute) ).
thf(19089,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( F @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( D @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( F @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3644]) ).
thf(3329,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) )
=> ( C @ ( A @ ( D @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageI) ).
thf(17796,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) )
=> ( C @ ( A @ ( D @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3329]) ).
thf(2258,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_fimplies @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) )
= ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__imp__eq) ).
thf(13477,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_fimplies @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) )
= ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2258]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(6051,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(3687,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I2_J) ).
thf(19261,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
& ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3687]) ).
thf(1810,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I3_J) ).
thf(11753,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1810]) ).
thf(3679,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).
thf(19221,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3679]) ).
thf(3375,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(17968,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3375]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
thf(5871,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(4674,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__sing) ).
thf(23079,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
=> ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4674]) ).
thf(4115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).
thf(20951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4115]) ).
thf(552,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__number__of__Bit0) ).
thf(6885,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(3470,axiom,
! [A: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__nat__eq) ).
thf(18373,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3470]) ).
thf(986,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__insort__insert) ).
thf(8466,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__insert__key ) ) ) ) @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(3619,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I22_J) ).
thf(18986,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3619]) ).
thf(2489,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(14485,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2489]) ).
thf(3842,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(19907,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3842]) ).
thf(4722,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton) ).
thf(23273,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4722]) ).
thf(2775,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanLessThan__empty) ).
thf(15608,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2775]) ).
thf(488,axiom,
! [A: $i,B: $i] : ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Oirrefl ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__diff__Id) ).
thf(6597,plain,
! [A: $i,B: $i] : ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Oirrefl ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(3846,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
thf(19925,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3846]) ).
thf(2796,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(15693,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2796]) ).
thf(4260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__inf__le__inf) ).
thf(21535,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4260]) ).
thf(3193,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expand__Suc) ).
thf(17276,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3193]) ).
thf(842,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Osublist ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__nil) ).
thf(7956,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Osublist ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(2477,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__sup__insert) ).
thf(14444,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2477]) ).
thf(2270,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
thf(13523,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2270]) ).
thf(1885,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__eq__Union__image) ).
thf(12056,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1885]) ).
thf(4504,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( A
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__empty2) ).
thf(22431,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( A
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4504]) ).
thf(3610,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert) ).
thf(18947,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3610]) ).
thf(2521,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(14624,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2521]) ).
thf(1298,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(9710,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Osort__key ) ) ) @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Osort__key ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__sort) ).
thf(4922,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Osort__key ) ) ) @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Osort__key ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(3852,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_COMBK ) @ hAPP ) @ ( tc_Nat_Onat @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__setsum) ).
thf(19954,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_COMBK ) @ hAPP ) @ ( tc_Nat_Onat @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3852]) ).
thf(3496,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omin @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).
thf(18490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omin @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3496]) ).
thf(4709,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__Diff__lessThan) ).
thf(23228,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4709]) ).
thf(3716,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).
thf(19377,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3716]) ).
thf(4434,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__empty) ).
thf(22192,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4434]) ).
thf(1370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(9953,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__take) ).
thf(7159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(561,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Olast ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__replicate) ).
thf(6921,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Olast ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(2242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
thf(13399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2242]) ).
thf(3608,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olistrel ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__subset) ).
thf(18940,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olistrel ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3608]) ).
thf(1053,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( B @ c_Relation_OId ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_relpow_Osimps_I1_J) ).
thf(8701,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( B @ c_Relation_OId ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(1536,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( H @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( G @ ( H @ c_Product__Type_OPair ) @ ( F @ ( G @ ( H @ tc_prod ) @ ( G @ tc_fun ) @ ( H @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ ( H @ tc_prod ) @ ( G @ c_COMBB ) ) @ ( F @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( C @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( C @ ( F @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map__map) ).
thf(10684,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( H @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( G @ ( H @ c_Product__Type_OPair ) @ ( F @ ( G @ ( H @ tc_prod ) @ ( G @ tc_fun ) @ ( H @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ ( H @ tc_prod ) @ ( G @ c_COMBB ) ) @ ( F @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ ( G @ ( C @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( C @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( C @ ( F @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536]) ).
thf(1261,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) )
& ( ( F = E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(9535,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) )
& ( ( F = E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(1518,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Int_OBit1 )
= ( A @ c_Int_OBit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).
thf(10572,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Int_OBit1 )
= ( A @ c_Int_OBit1 ) ) )
& ( ( ( B @ c_Int_OBit1 )
= ( A @ c_Int_OBit1 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ c_List_Ofoldr ) ) ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr1__lemma) ).
thf(5074,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ c_List_Ofoldr ) ) ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(1465,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(10371,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).
thf(3135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__one) ).
thf(17055,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3135]) ).
thf(4679,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).
thf(23104,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4679]) ).
thf(2251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ! [E: $i] :
( ( B @ ( C @ ( D @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( E @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__iff__zip) ).
thf(13435,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ! [E: $i] :
( ( B @ ( C @ ( D @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( E @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) )
=> ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( B @ ( C @ ( D @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( E @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2251]) ).
thf(2804,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
thf(15721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2804]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).
thf(5592,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(5980,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(3450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Oset @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ tc_List_Olist @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ ( C @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__mapI) ).
thf(18290,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Oset @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ tc_List_Olist @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ ( C @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3450]) ).
thf(4336,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I10_J) ).
thf(21846,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4336]) ).
thf(3011,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__1) ).
thf(16579,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3011]) ).
thf(2644,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc1) ).
thf(15122,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2644]) ).
thf(1145,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Osublists ) )
= ( C @ tc_List_Olist @ tc_List_Olist @ c_COMBI @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ ( C @ tc_List_Olist @ c_List_Oappend @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Enum_Osublists ) @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublists_Osimps_I2_J) ).
thf(9061,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Osublists ) )
= ( C @ tc_List_Olist @ tc_List_Olist @ c_COMBI @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ ( C @ tc_List_Olist @ c_List_Oappend @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Enum_Osublists ) @ ( C @ tc_List_Olist @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_List_Olist @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(1513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__ex ) ) )
<=> ( ( A @ ( C @ ( D @ c_List_Olist__ex ) ) )
| ( B @ ( C @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__simps_I1_J) ).
thf(10553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_List_Olist__ex ) ) )
| ( B @ ( C @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__ex ) ) ) )
& ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__ex ) ) )
=> ( ( A @ ( C @ ( D @ c_List_Olist__ex ) ) )
| ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513]) ).
thf(1242,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__dropWhile) ).
thf(9467,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(3940,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set_Ointros) ).
thf(20274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3940]) ).
thf(3937,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
~ ( B @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( C @ c_List_Olexord ) @ ( A @ ( A @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).
thf(20257,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
~ ( B @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( C @ c_List_Olexord ) @ ( A @ ( A @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3937]) ).
thf(1837,axiom,
tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
thf(11855,plain,
tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1837]) ).
thf(877,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zero) ).
thf(8096,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__power) ).
thf(4752,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4753,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_Rings_Oring__1 ) ),
inference(cnf,[status(esa)],[4752]) ).
thf(4754,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ class_Rings_Oring__1 )
| ( ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4753]) ).
thf(3148,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Odistrib__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf2__distrib) ).
thf(17105,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Odistrib__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3148]) ).
thf(4511,axiom,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
thf(22468,plain,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4511]) ).
thf(3311,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__infI2) ).
thf(17717,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3311]) ).
thf(2339,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).
thf(13813,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2339]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I36_J) ).
thf(4894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(2637,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
thf(15102,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2637]) ).
thf(2852,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( A @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I5_J) ).
thf(15924,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( A @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2852]) ).
thf(4036,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) )
= ( A @ ( c_fequal @ ( c_fconj @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__def_H) ).
thf(20590,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) )
= ( A @ ( c_fequal @ ( c_fconj @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4036]) ).
thf(1249,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int__left) ).
thf(9499,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(3862,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
thf(19993,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3862]) ).
thf(3504,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
thf(18509,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3504]) ).
thf(2593,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ ( B @ ( D @ c_List_Onth @ hAPP ) @ ( C @ ( D @ c_Product__Type_OPair ) @ ( tc_Nat_Onat @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ ( C @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ ( C @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( C @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_HOL_OEx @ ( C @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip) ).
thf(14902,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ ( B @ ( D @ c_List_Onth @ hAPP ) @ ( C @ ( D @ c_Product__Type_OPair ) @ ( tc_Nat_Onat @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ ( C @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ ( C @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( C @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_HOL_OEx @ ( C @ ( D @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2593]) ).
thf(4360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( A @ ( A @ ( C @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(21941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( A @ ( A @ ( C @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4360]) ).
thf(4560,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__empty1) ).
thf(22644,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4560]) ).
thf(3993,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Pow) ).
thf(20435,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3993]) ).
thf(954,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olexord ) @ ( B @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
~ ( A @ ( F @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ c_List_Olexord ) @ ( B @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).
thf(8350,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olexord ) @ ( B @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
~ ( A @ ( F @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ c_List_Olexord ) @ ( B @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__all ) ) )
<=> ( ( A @ ( C @ ( D @ c_List_Olist__all ) ) )
& ( B @ ( C @ ( D @ c_List_Olist__all ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__append) ).
thf(6481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_List_Olist__all ) ) )
& ( B @ ( C @ ( D @ c_List_Olist__all ) ) ) )
=> ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__all ) ) ) )
& ( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__all ) ) )
=> ( ( A @ ( C @ ( D @ c_List_Olist__all ) ) )
& ( B @ ( C @ ( D @ c_List_Olist__all ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(4393,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_List_Olists ) )
= ( tc_HOL_Obool @ ( A @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_List_Olist_ONil @ ( A @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__empty) ).
thf(22061,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_List_Olists ) )
= ( tc_HOL_Obool @ ( A @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_List_Olist_ONil @ ( A @ tc_List_Olist @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4393]) ).
thf(1684,axiom,
! [A: $i] :
( ( A @ class_Groups_Ogroup__add )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).
thf(11252,plain,
! [A: $i] :
( ( A @ class_Groups_Ogroup__add )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times_Oidem) ).
thf(8295,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(720,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
thf(7511,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(1368,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_List_Olex ) @ ( B @ tc_List_Olist @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex) ).
thf(9948,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_List_Olex ) @ ( B @ tc_List_Olist @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(4168,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
thf(21163,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4168]) ).
thf(3637,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Product__Type_OPair ) @ ( A @ ( B @ tc_prod ) @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) )
= ( A @ ( B @ tc_prod ) @ c_Fun_Oid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__Pair) ).
thf(19067,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Product__Type_OPair ) @ ( A @ ( B @ tc_prod ) @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) )
= ( A @ ( B @ tc_prod ) @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3637]) ).
thf(2263,axiom,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olistrel1 ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).
thf(13496,plain,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olistrel1 ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2263]) ).
thf(4321,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oremdups ) )
= ( A @ ( C @ c_List_Oremdups ) @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oremdups ) )
= ( A @ ( C @ c_List_Oremdups ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups_Osimps_I2_J) ).
thf(21789,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oremdups ) )
= ( A @ ( C @ c_List_Oremdups ) @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oremdups ) )
= ( A @ ( C @ c_List_Oremdups ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4321]) ).
thf(1443,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(10228,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(3164,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le) ).
thf(17187,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3164]) ).
thf(4114,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
thf(20948,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4114]) ).
thf(804,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).
thf(7811,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(4367,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
thf(21970,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4367]) ).
thf(1471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__ex ) ) )
<=> ( ( A @ ( C @ ( D @ c_List_Olist__ex ) ) )
| ( B @ ( C @ ( D @ c_List_Olist__ex ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__append) ).
thf(10392,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_List_Olist__ex ) ) )
| ( B @ ( C @ ( D @ c_List_Olist__ex ) ) ) )
=> ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__ex ) ) ) )
& ( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist__ex ) ) )
=> ( ( A @ ( C @ ( D @ c_List_Olist__ex ) ) )
| ( B @ ( C @ ( D @ c_List_Olist__ex ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(2597,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(14919,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2597]) ).
thf(3371,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(17943,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3371]) ).
thf(2668,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ c_Predicate_Oconversep ) ) @ ( B @ ( C @ c_Predicate_Oconversep ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__conversep) ).
thf(15220,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ c_Predicate_Oconversep ) ) @ ( B @ ( C @ c_Predicate_Oconversep ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2668]) ).
thf(3201,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atMost) ).
thf(17304,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3201]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) )
=> ( ( ( A
!= ( B @ tc_List_Olist @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) )
& ( ( A
= ( B @ tc_List_Olist @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__transpose__sorted) ).
thf(5790,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Orev @ hAPP ) @ ( tc_Nat_Onat @ c_List_Olinorder__class_Osorted ) )
=> ( ( ( A
!= ( B @ tc_List_Olist @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_List_Olist @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) )
& ( ( A
= ( B @ tc_List_Olist @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(810,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sgn) ).
thf(7832,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(1389,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(10027,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).
thf(2364,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__top )
=> ( ( B @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__top__right) ).
thf(13893,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__top )
=> ( ( B @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2364]) ).
thf(1675,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__def) ).
thf(11225,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675]) ).
thf(3303,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of) ).
thf(17689,plain,
! [A: $i] : ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3303]) ).
thf(2175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I15_J) ).
thf(13136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2175]) ).
thf(4384,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__empty) ).
thf(22033,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4384]) ).
thf(4528,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( C @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2I) ).
thf(22539,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( C @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4528]) ).
thf(4318,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
thf(21767,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4318]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( c_fequal @ ( A @ ( B @ ( B @ ( B @ c_Predicate_Opred__comp ) ) ) ) @ ( c_fequal @ ( B @ ( B @ ( B @ c_Predicate_Opred__comp ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__comp__r) ).
thf(5684,plain,
! [A: $i,B: $i] :
( ( c_fequal @ ( A @ ( B @ ( B @ ( B @ c_Predicate_Opred__comp ) ) ) ) @ ( c_fequal @ ( B @ ( B @ ( B @ c_Predicate_Opred__comp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(3028,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ! [F: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( A @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__is__Cons) ).
thf(16643,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ! [F: $i] :
( ( C @ ( D @ c_List_Oset @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( A @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3028]) ).
thf(4316,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ class_Enum_Oenum )
& ( C @ class_Enum_Oenum ) )
=> ( ( A @ ( C @ ( B @ tc_prod ) @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
<=> ( C @ ( B @ c_Product__Type_OPair ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( C @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( B @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__ex @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_enum__ex__prod__def) ).
thf(21760,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ class_Enum_Oenum )
& ( C @ class_Enum_Oenum ) )
=> ( ( ( C @ ( B @ c_Product__Type_OPair ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( C @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( B @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__ex @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ tc_prod ) @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( B @ tc_prod ) @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
=> ( C @ ( B @ c_Product__Type_OPair ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( C @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( B @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__ex @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4316]) ).
thf(1440,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__divide) ).
thf(10218,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(2110,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
thf(12841,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2110]) ).
thf(1156,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
thf(9121,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(3129,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ c_Relation_Oconverse ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseI) ).
thf(17034,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ c_Relation_Oconverse ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3129]) ).
thf(2380,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( A @ ( B @ ( E @ c_Relation_Orefl__on ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Relation_Orefl__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Un) ).
thf(13957,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( A @ ( B @ ( E @ c_Relation_Orefl__on ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Relation_Orefl__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2380]) ).
thf(2440,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) )
<=> ( ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__Cons) ).
thf(14272,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ c_List_Olinorder__class_Osorted ) ) )
=> ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) )
& ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2440]) ).
thf(1637,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Wellfounded_Oacc ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).
thf(11066,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Wellfounded_Oacc ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
thf(8612,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(3443,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_OremoveAll ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll_Osimps_I1_J) ).
thf(18271,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_OremoveAll ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3443]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanLessThan__int) ).
thf(8396,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1395,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(10048,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(3187,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__1) ).
thf(17255,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3187]) ).
thf(1925,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oeq__fold) ).
thf(12187,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1925]) ).
thf(3185,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_OF__eq) ).
thf(17249,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3185]) ).
thf(3393,axiom,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ ( B @ ( B @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__set__fold) ).
thf(18054,plain,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ ( B @ ( B @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3393]) ).
thf(2557,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD1) ).
thf(14778,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2557]) ).
thf(524,axiom,
( ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of )
= ( c_Int_Onat @ ( c_Code__Numeral_Oof__nat @ ( tc_Int_Oint @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__code__numeral__def) ).
thf(6762,plain,
( ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of )
= ( c_Int_Onat @ ( c_Code__Numeral_Oof__nat @ ( tc_Int_Oint @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(4684,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__left) ).
thf(23117,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4684]) ).
thf(2378,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ hAPP ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oremove) ).
thf(13948,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ hAPP ) )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2378]) ).
thf(4586,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__not__random__dseq ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ c_New__DSequence_Opos__not__seq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(22750,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__not__random__dseq ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ c_New__DSequence_Opos__not__seq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4586]) ).
thf(4210,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ c_List_Olists ) @ ( A @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__lists__eq) ).
thf(21333,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_List_Olists ) @ ( A @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_List_Olists ) @ ( A @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4210]) ).
thf(3558,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union) ).
thf(18758,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3558]) ).
thf(882,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).
thf(8111,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(1452,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).
thf(10328,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(1669,axiom,
( ( c_fTrue @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).
thf(11208,plain,
( ( c_fTrue @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669]) ).
thf(11209,plain,
( ( c_fTrue @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[11208]) ).
thf(43847,plain,
( ( c_fTrue @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Orderings_Obot__class_Obot ) ),
inference(rewrite,[status(thm)],[11209,20483]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__length__filter__compl) ).
thf(6036,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral1) ).
thf(5467,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(1607,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
thf(10952,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607]) ).
thf(199,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Pls) ).
thf(5420,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(3639,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus) ).
thf(19074,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3639]) ).
thf(2303,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
thf(13677,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2303]) ).
thf(2944,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).
thf(16295,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2944]) ).
thf(4304,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
| ( B @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__conjI) ).
thf(21708,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
| ( B @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4304]) ).
thf(3721,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( F @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_List_Olistrel1 ) @ ( F @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( F @ c_List_Olistrel1 ) @ ( F @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
thf(19397,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( F @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_List_Olistrel1 ) @ ( F @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( F @ c_List_Olistrel1 ) @ ( F @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3721]) ).
thf(3710,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) )
= ( c_Int_Onat @ ( A @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Set_OCollect @ hAPP ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).
thf(19349,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) )
= ( c_Int_Onat @ ( A @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Set_OCollect @ hAPP ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3710]) ).
thf(2335,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_ODomain ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
thf(13801,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_ODomain ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2335]) ).
thf(2071,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
<=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less) ).
thf(12720,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2071]) ).
thf(1462,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_List_Oupt ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).
thf(10360,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_List_Oupt ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(6545,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(4585,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__left) ).
thf(22747,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4585]) ).
thf(4714,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__left) ).
thf(23246,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4714]) ).
thf(2646,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__disjoint) ).
thf(15127,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2646]) ).
thf(24443,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,23913]) ).
thf(24444,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[24443]) ).
thf(24445,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[24444:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(24505,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[24445]) ).
thf(39018,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_c @ ( c_Int_OPls @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(rewrite,[status(thm)],[24505,7678]) ).
thf(45369,plain,
! [A: $i] :
( ( ( A @ ( v_c @ ( c_Int_OPls @ hAPP ) @ hAPP ) )
!= ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(paramod_ordered,[status(thm)],[8226,39018]) ).
thf(45472,plain,
! [A: $i] :
( ( A != c_Int_OPls )
| ( ( v_c @ ( c_Int_OPls @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[45369]) ).
thf(45793,plain,
( ( ( v_c @ ( c_Int_OPls @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[45472]) ).
thf(3877,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__inf__iff) ).
thf(20044,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3877]) ).
thf(1282,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Com_Ocom_Ocom__size @ ( B @ c_Com_Ocom_Ocom__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I4_J) ).
thf(9649,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Com_Ocom_Ocom__size @ ( B @ c_Com_Ocom_Ocom__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(4331,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Un) ).
thf(21831,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4331]) ).
thf(2689,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__absorb2) ).
thf(15288,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2689]) ).
thf(1520,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI__ex) ).
thf(10585,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).
thf(3945,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
thf(20287,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3945]) ).
thf(2165,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__subset__iff) ).
thf(13089,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2165]) ).
thf(4412,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff) ).
thf(22123,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4412]) ).
thf(3994,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__inter) ).
thf(20438,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3994]) ).
thf(3933,axiom,
c_Int_Ointrel @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Equiv__Relations_Oequiv ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__intrel) ).
thf(20247,plain,
c_Int_Ointrel @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Equiv__Relations_Oequiv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3933]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__number__of__Bit1) ).
thf(5912,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(4078,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Equiv__Relations_Ocongruent ) ) ) )
<=> ! [E: $i] :
( ( B @ ( E @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( A @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent__def) ).
thf(20760,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( B @ ( E @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( A @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Equiv__Relations_Ocongruent ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Equiv__Relations_Ocongruent ) ) ) )
=> ! [E: $i] :
( ( B @ ( E @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ ( A @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4078]) ).
thf(4060,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ ( G @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD_H) ).
thf(20670,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ ( G @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4060]) ).
thf(4317,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
thf(21764,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4317]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nat__number__of) ).
thf(5753,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(2941,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).
thf(16281,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2941]) ).
thf(4552,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( tc_HOL_Obool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( tc_HOL_Obool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( A @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conseq1) ).
thf(22623,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( tc_HOL_Obool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( tc_HOL_Obool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( A @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4552]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__0) ).
thf(7522,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(2544,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Groups_Oordered__ab__semigroup__add )
& ( E @ class_Groups_Ocomm__monoid__add ) )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono3) ).
thf(14728,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Groups_Oordered__ab__semigroup__add )
& ( E @ class_Groups_Ocomm__monoid__add ) )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2544]) ).
thf(3650,axiom,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2__eq__if) ).
thf(19106,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3650]) ).
thf(4182,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( E @ c_List_OremoveAll ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_List_OremoveAll ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__removeAll__inj__on) ).
thf(21225,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( E @ c_List_OremoveAll ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_List_OremoveAll ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4182]) ).
thf(1256,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).
thf(9518,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(3284,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__D) ).
thf(17632,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3284]) ).
thf(1545,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(10724,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545]) ).
thf(2648,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ c_HOL_OThe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__def) ).
thf(15132,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ c_HOL_OThe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2648]) ).
thf(2978,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma) ).
thf(16446,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2978]) ).
thf(4623,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( B @ ( A @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__comp__emptyL) ).
thf(22885,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( B @ ( A @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4623]) ).
thf(1420,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__append__conv2) ).
thf(10144,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( C
= ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(1438,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( A @ ( B @ ( E @ hAPP ) @ ( C @ ( F @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( E @ hAPP ) @ ( C @ ( F @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( E @ hAPP ) @ ( C @ ( F @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).
thf(10211,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__idem ) ) ) )
=> ( ( A @ ( B @ ( E @ hAPP ) @ ( C @ ( F @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( E @ hAPP ) @ ( C @ ( F @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( E @ hAPP ) @ ( C @ ( F @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).
thf(1264,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).
thf(9550,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(3418,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ c_COMBK ) @ hAPP ) @ ( D @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ c_COMBK ) @ hAPP ) @ ( D @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__const) ).
thf(18163,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ c_COMBK ) @ hAPP ) @ ( D @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ c_COMBK ) @ hAPP ) @ ( D @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3418]) ).
thf(3926,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
thf(20225,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm__idem ) ) )
=> ( ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3926]) ).
thf(3738,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
<=> ! [F: $i] :
( ( B @ ( E @ c_List_Oset @ hAPP ) @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( C @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__eq__conv) ).
thf(19470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( B @ ( E @ c_List_Oset @ hAPP ) @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( C @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
=> ! [F: $i] :
( ( B @ ( E @ c_List_Oset @ hAPP ) @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( C @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3738]) ).
thf(3341,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__least) ).
thf(17832,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3341]) ).
thf(2813,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).
thf(15753,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2813]) ).
thf(337,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).
thf(5948,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1916,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(12160,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1916]) ).
thf(2074,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atMost) ).
thf(12733,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2074]) ).
thf(1092,axiom,
! [A: $i] :
( ( A @ class_Lattices_Osemilattice__inf )
=> ( A @ c_Lattices_Osemilattice__inf__class_Oinf @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__inf) ).
thf(8845,plain,
! [A: $i] :
( ( A @ class_Lattices_Osemilattice__inf )
=> ( A @ c_Lattices_Osemilattice__inf__class_Oinf @ ( A @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(839,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).
thf(7947,plain,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(1103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ ( B @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ ( C @ tc_List_Olist @ ( D @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( C @ c_List_Omap ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__map) ).
thf(8917,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ ( B @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ ( C @ tc_List_Olist @ ( D @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( C @ c_List_Omap ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(2677,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
thf(15256,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2677]) ).
thf(1788,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
thf(11674,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1788]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OnegDivAlg ) )
= ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OnegDivAlg ) )
= ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn__number__of) ).
thf(5030,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OnegDivAlg ) )
= ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Divides_OnegDivAlg ) )
= ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(2962,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ ( E @ ( A @ ( B @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep_Ointros) ).
thf(16374,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ ( E @ ( A @ ( B @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2962]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I38_J) ).
thf(5203,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(171,axiom,
! [A: $i] :
( ( A @ c_Int_Opred @ c_Int_Osucc )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__pred) ).
thf(5309,plain,
! [A: $i] :
( ( A @ c_Int_Opred @ c_Int_Osucc )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(4342,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( E @ ( B @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( E @ c_Fun_Obij__betw ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__comp) ).
thf(21863,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( E @ ( B @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( E @ c_Fun_Obij__betw ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4342]) ).
thf(1982,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__subtractf) ).
thf(12396,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1982]) ).
thf(1772,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__subtractf) ).
thf(11622,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772]) ).
thf(2495,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).
thf(14513,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2495]) ).
thf(2985,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(16478,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2985]) ).
thf(4197,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).
thf(21283,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4197]) ).
thf(3860,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( tc_HOL_Obool @ ( C @ ( F @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( D @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( B @ ( E @ tc_prod ) @ ( C @ ( F @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( E @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__surj) ).
thf(19988,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( tc_HOL_Obool @ ( C @ ( F @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( D @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( B @ ( E @ tc_prod ) @ ( C @ ( F @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( E @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3860]) ).
thf(3144,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc__Suc) ).
thf(17092,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3144]) ).
thf(1671,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(11213,plain,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671]) ).
thf(4289,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
<=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__empty__conv) ).
thf(21650,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4289]) ).
thf(968,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(8391,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__frac__eq) ).
thf(8248,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ ( F @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) ) )
<=> ( ( B @ ( F @ ( D @ c_Product__Type_Osnd ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( F @ ( D @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__eq__conv) ).
thf(5001,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( B @ ( F @ ( D @ c_Product__Type_Osnd ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( F @ ( D @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ hAPP ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ ( F @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ ( F @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) ) )
=> ( ( B @ ( F @ ( D @ c_Product__Type_Osnd ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( F @ ( D @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(2831,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_ORange ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id__on) ).
thf(15846,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_ORange ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2831]) ).
thf(2569,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).
thf(14832,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2569]) ).
thf(3249,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__fold__insert) ).
thf(17500,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3249]) ).
thf(3430,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__replicate) ).
thf(18230,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3430]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1) ).
thf(4982,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(2650,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__sign) ).
thf(15148,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2650]) ).
thf(2022,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Relation_OId__on ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
!= ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__onE) ).
thf(12529,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Relation_OId__on ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
!= ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2022]) ).
thf(3043,axiom,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Set_OPow @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Pow__Union) ).
thf(16710,plain,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Set_OPow @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3043]) ).
thf(4207,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplI) ).
thf(21324,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4207]) ).
thf(1777,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__1__number__of) ).
thf(11637,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777]) ).
thf(3472,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(18387,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3472]) ).
thf(4106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I20_J) ).
thf(20919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4106]) ).
thf(3327,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__inv__eq) ).
thf(17790,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3327]) ).
thf(4473,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OemptyI) ).
thf(22327,plain,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4473]) ).
thf(1865,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionI) ).
thf(11969,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1865]) ).
thf(1332,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( F @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( E @ ( C @ ( G @ ( F @ c_COMBB ) ) @ ( G @ ( G @ ( C @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ tc_fun ) @ ( G @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( C @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__map) ).
thf(9807,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( F @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( E @ ( C @ ( G @ ( F @ c_COMBB ) ) @ ( G @ ( G @ ( C @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ tc_fun ) @ ( G @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( C @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) ) )
<=> ( A
= ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__rev__conv) ).
thf(5450,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) ) ) )
& ( ( ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) ) )
=> ( A
= ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(2828,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_OtakeWhile ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__takeWhileD) ).
thf(15836,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_OtakeWhile ) ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2828]) ).
thf(1234,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
thf(9435,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(3350,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oremove) ).
thf(17864,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3350]) ).
thf(1501,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Osingle__valued ) ) )
=> ( ( A @ ( B @ ( D @ c_Relation_Osingle__valued ) ) )
=> ( A @ ( C @ ( B @ ( D @ ( E @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Relation_Osingle__valued ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__rel__comp) ).
thf(10509,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Osingle__valued ) ) )
=> ( ( A @ ( B @ ( D @ c_Relation_Osingle__valued ) ) )
=> ( A @ ( C @ ( B @ ( D @ ( E @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Relation_Osingle__valued ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501]) ).
thf(4191,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I4_J) ).
thf(21266,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4191]) ).
thf(4591,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
thf(22764,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4591]) ).
thf(3566,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__diff__subset) ).
thf(18788,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3566]) ).
thf(589,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__0) ).
thf(7009,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(2184,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Oremove1 ) ) @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remove1__subset) ).
thf(13185,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Oremove1 ) ) @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2184]) ).
thf(4704,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty) ).
thf(23209,plain,
! [A: $i,B: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4704]) ).
thf(1735,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc__Cons) ).
thf(11475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735]) ).
thf(3527,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(18593,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3527]) ).
thf(3071,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__injective) ).
thf(16811,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3071]) ).
thf(3770,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
thf(19613,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3770]) ).
thf(3987,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert__remove) ).
thf(20420,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3987]) ).
thf(780,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I1_J) ).
thf(7737,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(904,axiom,
! [A: $i] :
( c_Int_OMin
!= ( A @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).
thf(8185,plain,
! [A: $i] :
( c_Int_OMin
!= ( A @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(3627,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( D @ ( F @ c_Set_Ovimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__compose) ).
thf(19031,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( D @ ( F @ c_Set_Ovimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3627]) ).
thf(2696,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__setsum) ).
thf(15304,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( C @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2696]) ).
thf(4215,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).
thf(21347,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4215]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OnegDivAlg ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Divides_OnegDivAlg ) @ ( A @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OnegDivAlg ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Osimps) ).
thf(5319,plain,
! [A: $i,B: $i] :
( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OnegDivAlg ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Divides_OnegDivAlg ) @ ( A @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OnegDivAlg ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(2276,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__idem) ).
thf(13545,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2276]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Osucc @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit1) ).
thf(5147,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Osucc @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1707,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(11354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707]) ).
thf(3534,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(18615,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3534]) ).
thf(4678,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__right) ).
thf(23101,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4678]) ).
thf(2632,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_Set_Oinsert @ ( C @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( D @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ tc_fun ) @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__def) ).
thf(15084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_Set_Oinsert @ ( C @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( D @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ tc_fun ) @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2632]) ).
thf(2759,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( B @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( B @ c_Fun_Oid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I1_J) ).
thf(15557,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( B @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( B @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2759]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_COMBI @ ( B @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).
thf(6188,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_COMBI @ ( B @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(4708,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( C
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( D @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__const) ).
thf(23225,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( C
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( D @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4708]) ).
thf(4571,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff) ).
thf(22696,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4571]) ).
thf(1610,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
thf(10964,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610]) ).
thf(2826,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ c_Set_OPow @ hAPP ) @ ( B @ ( D @ c_Set_OPow @ hAPP ) @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__mono) ).
thf(15828,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ c_Set_OPow @ hAPP ) @ ( B @ ( D @ c_Set_OPow @ hAPP ) @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2826]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(6415,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(2254,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( E @ ( B @ ( C @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( D @ ( B @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) ) ) )
& ( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( E @ ( B @ ( C @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__image) ).
thf(13461,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( E @ ( B @ ( C @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( D @ ( B @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) ) ) )
& ( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( E @ ( B @ ( C @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2254]) ).
thf(1664,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) )
= C )
<=> ( ( B @ ( C @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(11181,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( B @ ( C @ hAPP ) )
= A )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) )
= C ) )
& ( ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) )
= C )
=> ( ( B @ ( C @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664]) ).
thf(1244,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__upto) ).
thf(9486,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(3631,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__Un) ).
thf(19046,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3631]) ).
thf(3851,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(19952,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3851]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_OremoveAll ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__removeAll) ).
thf(8316,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_OremoveAll ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(3946,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ ( D @ c_HOL_OThe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__def) ).
thf(20289,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold__graph ) ) ) ) @ ( D @ c_HOL_OThe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3946]) ).
thf(2385,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeast) ).
thf(13983,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2385]) ).
thf(1983,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
thf(12399,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1983]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__map) ).
thf(6825,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(3143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion) ).
thf(17089,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3143]) ).
thf(1993,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( C @ ( B @ c_Relation_ODomain ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__def) ).
thf(12439,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( C @ ( B @ c_Relation_ODomain ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1993]) ).
thf(4111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( C @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
thf(20938,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( C @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4111]) ).
thf(3146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
thf(17099,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3146]) ).
thf(4514,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__0) ).
thf(22475,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4514]) ).
thf(2607,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omember__def) ).
thf(14960,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_List_Omember @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2607]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Com_Ocom_Ocom__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I3_J) ).
thf(5628,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ c_Com_Ocom_Ocom__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Com_Ocom_Ocom__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1830,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ ( D @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose ) )
= ( A @ ( C @ c_List_Otranspose ) @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ ( D @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__map__map) ).
thf(11835,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ ( D @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose ) )
= ( A @ ( C @ c_List_Otranspose ) @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ ( D @ tc_List_Olist @ ( C @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1830]) ).
thf(1679,axiom,
! [A: $i,B: $i] :
~ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist__ex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__simps_I2_J) ).
thf(11240,plain,
! [A: $i,B: $i] :
~ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist__ex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679]) ).
thf(4251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).
thf(21505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4251]) ).
thf(2867,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplE) ).
thf(15982,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2867]) ).
thf(2087,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__atMost) ).
thf(12771,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2087]) ).
thf(2248,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I21_J) ).
thf(13421,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2248]) ).
thf(3273,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( G @ c_Product__Type_OPair ) @ ( F @ ( G @ tc_prod ) @ c_member @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( F @ ( G @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ ( F @ ( G @ tc_prod ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ ( G @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Predicate_Opred__comp ) ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( D @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp__rel__comp__eq) ).
thf(17584,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( G @ c_Product__Type_OPair ) @ ( F @ ( G @ tc_prod ) @ c_member @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( F @ ( G @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ ( F @ ( G @ tc_prod ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ ( G @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Predicate_Opred__comp ) ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( G @ c_Product__Type_OPair ) @ ( F @ ( G @ tc_prod ) @ c_member @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( F @ ( G @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ ( F @ ( G @ tc_prod ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ ( G @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ ( G @ tc_prod ) @ tc_fun ) @ ( G @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Predicate_Opred__comp ) ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3273]) ).
thf(1738,axiom,
! [A: $i,B: $i] :
( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OposDivAlg ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Divides_OposDivAlg ) @ ( A @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OposDivAlg ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Osimps) ).
thf(11486,plain,
! [A: $i,B: $i] :
( ( ~ ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OposDivAlg ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Divides_OposDivAlg ) @ ( A @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Divides_OposDivAlg ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738]) ).
thf(3512,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( E @ ( B @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__comp) ).
thf(18547,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( E @ ( B @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3512]) ).
thf(3126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__mono) ).
thf(17025,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3126]) ).
thf(4564,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(22665,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4564]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( C @ ( H @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( G @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ ( H @ c_Product__Type_OPair ) @ ( D @ ( G @ ( H @ tc_prod ) @ ( G @ tc_fun ) @ ( H @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( G @ ( F @ ( G @ ( H @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( F @ ( G @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( G @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__zip__map) ).
thf(7515,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( C @ ( H @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( G @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ ( H @ c_Product__Type_OPair ) @ ( D @ ( G @ ( H @ tc_prod ) @ ( G @ tc_fun ) @ ( H @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( G @ ( F @ ( G @ ( H @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( F @ ( G @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( G @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( G @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(33080,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5382,26733]) ).
thf(33081,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Oring__1 )
!= ( A @ class_Rings_Oring__1 ) )
| ( ( A @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33080]) ).
thf(33082,plain,
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(pattern_uni,[status(thm)],[33081:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(39015,plain,
( ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert ) )
| ( ( v_c @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
| ( ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int )
!= ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Int_OPls @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(rewrite,[status(thm)],[33082,7678]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
thf(6803,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(33142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(paramod_ordered,[status(thm)],[4775,4729]) ).
thf(33410,plain,
! [C: $i,B: $i,A: $i] :
( ( A != v_c )
| ( ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33142]) ).
thf(33637,plain,
! [B: $i,A: $i] :
( ( ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( v_c @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33410]) ).
thf(735,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Osym ) )
=> ( A @ ( C @ ( B @ ( D @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__inv__image) ).
thf(7580,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Osym ) )
=> ( A @ ( C @ ( B @ ( D @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(3012,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).
thf(16582,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3012]) ).
thf(3381,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Oirrefl ) )
<=> ! [C: $i] :
~ ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
thf(17992,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Relation_Oirrefl ) ) )
& ( ( A @ ( B @ c_Relation_Oirrefl ) )
=> ! [C: $i] :
~ ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3381]) ).
thf(1416,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist_Olist__size ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ ( D @ c_List_Olist_Olist__size ) ) @ ( B @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I2_J) ).
thf(10128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist_Olist__size ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ ( D @ c_List_Olist_Olist__size ) ) @ ( B @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Oupt ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).
thf(6601,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_List_Oupt ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(1613,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
<=> ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__eq__Nil) ).
thf(10973,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
=> ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613]) ).
thf(3042,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__UN) ).
thf(16707,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3042]) ).
thf(2551,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_List_Olinorder__class_Osorted__list__of__set ) )
= ( A @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__empty) ).
thf(14755,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_List_Olinorder__class_Osorted__list__of__set ) )
= ( A @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2551]) ).
thf(2459,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( D @ c_Wellfounded_Omax__ext ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).
thf(14359,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( D @ c_Wellfounded_Omax__ext ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2459]) ).
thf(1343,axiom,
tc_Int_Oint @ class_Groups_Olinordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).
thf(9851,plain,
tc_Int_Oint @ class_Groups_Olinordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult) ).
thf(7251,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1216,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(9353,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__conv) ).
thf(5998,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(3781,axiom,
! [A: $i,B: $i] : ( A @ ( A @ ( B @ c_Fun_Oid @ ( B @ ( B @ c_Fun_Obij__betw ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__id) ).
thf(19656,plain,
! [A: $i,B: $i] : ( A @ ( A @ ( B @ c_Fun_Oid @ ( B @ ( B @ c_Fun_Obij__betw ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3781]) ).
thf(2217,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) )
<=> ( ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
& ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_Oequations_I2_J) ).
thf(13299,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
& ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) )
& ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
& ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2217]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Orev @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
thf(5613,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Orev @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__conv) ).
thf(5240,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( E @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(2315,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter) ).
thf(13724,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2315]) ).
thf(1843,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ ( G @ ( E @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) @ ( F @ ( G @ c_Product__Type_Ofst ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__map__pair) ).
thf(11882,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ ( G @ ( E @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) @ ( F @ ( G @ c_Product__Type_Ofst ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1843]) ).
thf(2115,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( c_Int_OInteg @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( c_Int_OAbs__Integ @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__induct) ).
thf(12868,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( c_Int_OInteg @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( c_Int_OAbs__Integ @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2115]) ).
thf(3769,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Diff__eq) ).
thf(19610,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3769]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_List_Ofoldl ) ) ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_start__le__sum) ).
thf(6479,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_List_Ofoldl ) ) ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(2664,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold_H) ).
thf(15208,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2664]) ).
thf(4454,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton) ).
thf(22262,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4454]) ).
thf(1189,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(9247,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1876,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__left__idem) ).
thf(12014,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1876]) ).
thf(4125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__Un__disjoint) ).
thf(20987,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4125]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__mult) ).
thf(5504,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(2673,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Ovimage ) ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__INT) ).
thf(15240,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Ovimage ) ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2673]) ).
thf(2181,axiom,
! [A: $i] :
( ( A @ c_Nitpick_Ozero__frac )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ c_Nitpick_OAbs__Frac ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ozero__frac__def) ).
thf(13175,plain,
! [A: $i] :
( ( A @ c_Nitpick_Ozero__frac )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ c_Nitpick_OAbs__Frac ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2181]) ).
thf(3666,axiom,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(19169,plain,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3666]) ).
thf(2600,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__infinite) ).
thf(14931,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2600]) ).
thf(3493,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).
thf(18478,plain,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3493]) ).
thf(4261,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__inf__bot) ).
thf(21537,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4261]) ).
thf(4526,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
<=> ( ( B = A )
& ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton__iff) ).
thf(22526,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = A )
& ( C = B ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
=> ( ( B = A )
& ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4526]) ).
thf(1586,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( B @ ( tc_HOL_Obool @ c_COMBK ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( B @ c_Random_Opick ) )
= ( A @ ( B @ c_Random_Opick ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick__drop__zero) ).
thf(10860,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( B @ ( tc_HOL_Obool @ c_COMBK ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Ofilter ) @ hAPP ) @ ( B @ c_Random_Opick ) )
= ( A @ ( B @ c_Random_Opick ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586]) ).
thf(3729,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(19435,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3729]) ).
thf(3857,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__absorb) ).
thf(19976,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3857]) ).
thf(3058,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
thf(16763,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3058]) ).
thf(3804,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(19742,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3804]) ).
thf(4227,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__compl__top) ).
thf(21397,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4227]) ).
thf(3830,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).
thf(19833,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3830]) ).
thf(3190,axiom,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(17262,plain,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3190]) ).
thf(1700,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).
thf(11334,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).
thf(3874,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_COMBK ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).
thf(20030,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_COMBK ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3874]) ).
thf(691,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I13_J) ).
thf(7374,plain,
! [A: $i] :
( ( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(1706,axiom,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__power2) ).
thf(11351,plain,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706]) ).
thf(3102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(16934,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3102]) ).
thf(1828,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(11825,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1828]) ).
thf(3336,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I6_J) ).
thf(17817,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3336]) ).
thf(1227,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Equiv__Relations_Oequivp ) )
=> ( A @ ( B @ c_Equiv__Relations_Opart__equivp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__implies__part__equivp) ).
thf(9406,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Equiv__Relations_Oequivp ) )
=> ( A @ ( B @ c_Equiv__Relations_Opart__equivp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(1444,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Bit0) ).
thf(10231,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(4443,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__insert) ).
thf(22222,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4443]) ).
thf(881,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg) ).
thf(8108,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_List_Orev @ hAPP ) @ ( C @ ( E @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ ( E @ ( D @ c_List_Ofoldr ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr) ).
thf(5364,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_List_Orev @ hAPP ) @ ( C @ ( E @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ ( E @ ( D @ c_List_Ofoldr ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(3398,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(18066,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3398]) ).
thf(3664,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__upt) ).
thf(19164,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3664]) ).
thf(2836,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fNot @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) )
= ( A @ ( B @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
thf(15860,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fNot @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) )
= ( A @ ( B @ c_Set_OCollect @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2836]) ).
thf(1593,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__upto) ).
thf(10884,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).
thf(2642,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fdisj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__compr) ).
thf(15116,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fdisj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2642]) ).
thf(2572,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(14838,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2572]) ).
thf(2558,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( A @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite__subset) ).
thf(14781,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( A @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2558]) ).
thf(1484,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__map) ).
thf(10432,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484]) ).
thf(1270,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div) ).
thf(9574,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(3712,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc2) ).
thf(19363,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3712]) ).
thf(2345,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).
thf(13831,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2345]) ).
thf(1197,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Product__Type_Ofst ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__conv) ).
thf(9274,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Product__Type_Ofst ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(3436,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(18246,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3436]) ).
thf(1861,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__absorb) ).
thf(11957,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1861]) ).
thf(4290,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold_H) ).
thf(21661,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4290]) ).
thf(2172,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(13119,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2172]) ).
thf(3657,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
thf(19132,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3657]) ).
thf(411,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Omax__ext ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__wf) ).
thf(6245,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Omax__ext ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(3965,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__image__Compl__eq) ).
thf(20343,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3965]) ).
thf(387,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__div__nat__number__of) ).
thf(6161,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(2878,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= B )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( F @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
thf(16014,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= B )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( F @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2878]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
thf(7498,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(1842,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oconcat ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__concat) ).
thf(11879,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oconcat ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1842]) ).
thf(1648,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( B
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
thf(11108,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648]) ).
thf(3659,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Odistrib__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup1__distrib) ).
thf(19137,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Odistrib__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3659]) ).
thf(4794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( D @ c_Int_Oring__1__class_Oof__int @ ( C @ ( D @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( D @ class_Rings_Oring__1 ) ),
inference(cnf,[status(esa)],[4793]) ).
thf(4795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ class_Rings_Oring__1 )
| ( ( A @ ( B @ ( tc_Int_Oint @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( B @ ( D @ c_Int_Oring__1__class_Oof__int @ ( C @ ( D @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4794]) ).
thf(2550,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ? [E: $i] : ( A @ ( C @ ( E @ ( B @ ( D @ c_Fun_Obij__betw ) ) ) ) )
<=> ( ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BIJ) ).
thf(14749,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) ) )
=> ? [E: $i] : ( A @ ( C @ ( E @ ( B @ ( D @ c_Fun_Obij__betw ) ) ) ) ) )
& ( ? [E: $i] : ( A @ ( C @ ( E @ ( B @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2550]) ).
thf(4642,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__no__loop) ).
thf(22971,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4642]) ).
thf(2803,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
thf(15717,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2803]) ).
thf(4135,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb1) ).
thf(21028,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4135]) ).
thf(2426,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
thf(14202,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2426]) ).
thf(2055,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I6_J) ).
thf(12665,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2055]) ).
thf(2497,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
thf(14518,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2497]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
thf(5895,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(3751,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(19527,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3751]) ).
thf(4232,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( E @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) )
=> ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__partition) ).
thf(21423,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( E @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) )
=> ( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4232]) ).
thf(766,axiom,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Nat__Transfer_Ois__nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J) ).
thf(7690,plain,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Nat__Transfer_Ois__nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(3319,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ ( D @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__take__subset__set__take) ).
thf(17750,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ ( D @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3319]) ).
thf(2517,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less) ).
thf(14607,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2517]) ).
thf(3313,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ ( B @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Fun_Oinj__on ) ) ) )
<=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__map) ).
thf(17721,plain,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ ( B @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Fun_Oinj__on ) ) ) ) )
& ( ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_List_Omap ) @ hAPP ) @ ( B @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3313]) ).
thf(2808,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__map__eq__map) ).
thf(15731,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2808]) ).
thf(33139,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
| ~ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(paramod_ordered,[status(thm)],[4775,4729]) ).
thf(33579,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( v_c @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( A @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33139]) ).
thf(33806,plain,
! [B: $i,A: $i] :
( ( ( B @ ( v_c @ ( A @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) )
!= ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
| ~ ( tc_HOL_Obool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( v_G @ ( t_a @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(simp,[status(thm)],[33579]) ).
thf(3037,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_Option_Ooption @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_Option_Ooption @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
thf(16675,plain,
! [A: $i] :
( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( A @ tc_Option_Ooption @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_Option_Ooption @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( A @ tc_Option_Ooption @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_Option_Ooption @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3037]) ).
thf(1237,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__take) ).
thf(9453,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(4272,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__fun__def) ).
thf(21586,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4272]) ).
thf(2387,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__inter) ).
thf(13994,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2387]) ).
thf(2881,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ? [E: $i] :
( ( A @ ( C @ ( E @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) )
<=> ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
thf(16029,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( A @ ( C @ ( E @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) ) )
& ( ? [E: $i] :
( ( A @ ( C @ ( E @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) )
=> ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( C @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2881]) ).
thf(581,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(6992,plain,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(3549,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oinsert__remove) ).
thf(18707,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3549]) ).
thf(19045,plain,
~ ( c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(polarity_switch,[status(thm)],[19044]) ).
thf(26623,plain,
( ( ( c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8089,19045]) ).
thf(26624,plain,
( ( c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[26623]) ).
thf(26628,plain,
( ( c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) )
!= c_fTrue ),
inference(simp,[status(thm)],[26624]) ).
thf(1625,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__upt) ).
thf(11017,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625]) ).
thf(4219,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Relation_Oconverse ) @ ( C @ ( tc_HOL_Obool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__INTER) ).
thf(21362,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Relation_Oconverse ) @ ( C @ ( tc_HOL_Obool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4219]) ).
thf(647,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ c_List_Oreplicate ) ) )
= ( A @ ( B @ ( c_fequal @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__length__filter) ).
thf(7224,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ c_List_Oreplicate ) ) )
= ( A @ ( B @ ( c_fequal @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(978,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__length) ).
thf(8431,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(4361,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__right) ).
thf(21945,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4361]) ).
thf(443,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(6420,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(3138,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Big__Operators_Olinorder__class_OMin ) )
= ( A @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_OF__eq) ).
thf(17067,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Big__Operators_Olinorder__class_OMin ) )
= ( A @ ( B @ c_Orderings_Oord__class_Omin @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3138]) ).
thf(1850,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__if) ).
thf(11921,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1850]) ).
thf(1711,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq) ).
thf(11369,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
& ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__map) ).
thf(7380,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
& ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
& ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(1321,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).
thf(9770,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(2735,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__disj) ).
thf(15469,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2735]) ).
thf(2561,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
=> ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_Equiv__Relations_Oequiv ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__listrel) ).
thf(14791,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
=> ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_Equiv__Relations_Oequiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2561]) ).
thf(1050,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rotate) ).
thf(8681,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(2331,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_Relation_Orefl__on ) ) ) )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__INTER) ).
thf(13784,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_Relation_Orefl__on ) ) ) )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2331]) ).
thf(1087,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) )
= ( B @ ( C @ c_Product__Type_OPair ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ ( C @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__Eps) ).
thf(8830,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) )
= ( B @ ( C @ c_Product__Type_OPair ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ ( C @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(2483,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist__ex ) ) )
<=> ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__iff__raw) ).
thf(14464,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Olist__ex ) ) ) )
& ( ( A @ ( B @ ( C @ c_List_Olist__ex ) ) )
=> ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2483]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(6706,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(4059,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( ( A @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ ( A @ c_Orderings_Oord_Omin ) )
= ( A @ c_Orderings_Oord__class_Omax ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dual__min) ).
thf(20667,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( ( A @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ ( A @ c_Orderings_Oord_Omin ) )
= ( A @ c_Orderings_Oord__class_Omax ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4059]) ).
thf(2478,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).
thf(14447,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2478]) ).
thf(2153,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( D != C ) )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( G @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( G @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__E2) ).
thf(13036,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( D != C ) )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( G @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( G @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2153]) ).
thf(3070,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__subset__iff) ).
thf(16807,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3070]) ).
thf(2506,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(14554,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2506]) ).
thf(3487,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ c_Relation_ODomain ) @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainI) ).
thf(18443,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ c_Relation_ODomain ) @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3487]) ).
thf(4127,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).
thf(20996,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4127]) ).
thf(3000,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).
thf(16550,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3000]) ).
thf(2911,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons__number__of) ).
thf(16153,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2911]) ).
thf(2596,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Oantisym ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisymD) ).
thf(14916,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Oantisym ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2596]) ).
thf(3649,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) )
=> ( A @ ( C @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__exp) ).
thf(19104,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Owf ) )
=> ( A @ ( C @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3649]) ).
thf(2401,axiom,
! [A: $i,B: $i] :
( ( B = A )
<=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I3_J) ).
thf(14058,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2401]) ).
thf(755,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exI__realizer) ).
thf(7659,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Product__Type_Ofst ) @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Product__Type_Osnd ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(1839,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) )
<=> ( ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( D @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
& ( B @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__append) ).
thf(11862,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( D @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
& ( B @ ( C @ c_List_Olinorder__class_Osorted ) ) )
=> ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) ) )
& ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( D @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
& ( B @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1839]) ).
thf(2545,axiom,
( ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__atMost__UNIV) ).
thf(14732,plain,
( ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2545]) ).
thf(626,axiom,
! [A: $i] :
( ( c_Int_OPls
= ( A @ c_Int_OBit0 ) )
<=> ( c_Int_OPls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).
thf(7146,plain,
! [A: $i] :
( ( ( c_Int_OPls = A )
=> ( c_Int_OPls
= ( A @ c_Int_OBit0 ) ) )
& ( ( c_Int_OPls
= ( A @ c_Int_OBit0 ) )
=> ( c_Int_OPls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(2429,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) )
<=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
thf(14219,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2429]) ).
thf(1552,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zmod) ).
thf(10744,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552]) ).
thf(4615,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Un) ).
thf(22862,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4615]) ).
thf(3184,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
thf(17247,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3184]) ).
thf(1546,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__replicate__const) ).
thf(10727,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546]) ).
thf(2448,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
thf(14306,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2448]) ).
thf(1112,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I8_J) ).
thf(8946,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(2504,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
thf(14543,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2504]) ).
thf(1964,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) ).
thf(12343,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1964]) ).
thf(4381,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib) ).
thf(22018,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4381]) ).
thf(4048,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD1) ).
thf(20639,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4048]) ).
thf(2532,axiom,
( c_Int_OInteg
= ( c_Int_Ointrel @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Integ__def) ).
thf(14678,plain,
( c_Int_OInteg
= ( c_Int_Ointrel @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2532]) ).
thf(1406,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] : ( E @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
thf(10082,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( E @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL )
=> ? [E: $i] : ( E @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( G @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
<=> ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( G @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__map1) ).
thf(4851,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( G @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_List_Olist__all2 ) ) ) ) )
=> ( A @ ( B @ ( C @ ( G @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( G @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
=> ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( G @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_List_Olist__all2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(2436,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oall__interval__nat ) ) )
<=> ! [D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__interval__nat__def) ).
thf(14242,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Oall__interval__nat ) ) ) )
& ( ( A @ ( B @ ( C @ c_List_Oall__interval__nat ) ) )
=> ! [D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2436]) ).
thf(2955,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(16350,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2955]) ).
thf(2566,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( A @ ( B @ ( C @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [H: $i] :
( ( A
= ( H @ ( C @ ( E @ hAPP ) @ hAPP ) ) )
=> ~ ( H @ ( B @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).
thf(14819,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( A @ ( B @ ( C @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [H: $i] :
( ( A
= ( H @ ( C @ ( E @ hAPP ) @ hAPP ) ) )
=> ~ ( H @ ( B @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2566]) ).
thf(3315,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( ( D @ ( B @ hAPP ) )
= A )
& ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__val__lemma) ).
thf(17728,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( ( D @ ( B @ hAPP ) )
= A )
& ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3315]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).
thf(6985,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__triv) ).
thf(6758,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(3355,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( D @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( B @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Product__Type_Ofst ) @ ( B @ ( C @ ( B @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= A ) )
& ( ( D
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( D @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( B @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Product__Type_Ofst ) @ ( B @ ( C @ ( B @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__image__times) ).
thf(17881,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( D @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( B @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Product__Type_Ofst ) @ ( B @ ( C @ ( B @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= A ) )
& ( ( D
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( D @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( C @ ( B @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Product__Type_Ofst ) @ ( B @ ( C @ ( B @ tc_prod ) @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3355]) ).
thf(1971,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
thf(12360,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1971]) ).
thf(2570,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olistsp ) @ ( B @ ( C @ c_List_Olistsp ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__mono) ).
thf(14834,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olistsp ) @ ( B @ ( C @ c_List_Olistsp ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2570]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons__number__of) ).
thf(7177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit1) ).
thf(6408,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(4580,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(22728,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) ) )
& ( ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4580]) ).
thf(3414,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__setprod) ).
thf(18149,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3414]) ).
thf(2711,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil2) ).
thf(15377,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2711]) ).
thf(2534,axiom,
! [A: $i] :
( ? [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL )
<=> ? [B: $i] :
( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat) ).
thf(14683,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL ) )
& ( ? [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2534]) ).
thf(3935,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head) ).
thf(20251,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3935]) ).
thf(1749,axiom,
tc_Product__Type_Ounit @ class_Nat_Osize,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Nat_Osize) ).
thf(11530,plain,
tc_Product__Type_Ounit @ class_Nat_Osize,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749]) ).
thf(2473,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Oantisym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id__on) ).
thf(14432,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Oantisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2473]) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Ois__nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).
thf(6041,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_Nat__Transfer_Ois__nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(4507,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ( A
= ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty__iff) ).
thf(22440,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A
= ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4507]) ).
thf(1276,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(9628,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(4353,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( C @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [G: $i,H: $i,I: $i] :
( ( D
= ( I @ ( G @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( H @ ( G @ ( C @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( I @ ( H @ ( E @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__compE) ).
thf(21910,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( C @ ( F @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [G: $i,H: $i,I: $i] :
( ( D
= ( I @ ( G @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( H @ ( G @ ( C @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( I @ ( H @ ( E @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4353]) ).
thf(2750,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Big__Operators_Olinorder__class_OMax ) )
= ( A @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_OF__eq) ).
thf(15525,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Big__Operators_Olinorder__class_OMax ) )
= ( A @ ( B @ c_Orderings_Oord__class_Omax @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2750]) ).
thf(4763,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ class_Rings_Olinordered__idom ) ),
inference(cnfConj,[status(thm)],[4762]) ).
thf(3923,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__quotient) ).
thf(20214,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3923]) ).
thf(3808,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Ovimage ) ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UN) ).
thf(19756,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ c_Set_Ovimage ) ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3808]) ).
thf(1819,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__rev) ).
thf(11789,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1819]) ).
thf(2669,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton) ).
thf(15223,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2669]) ).
thf(3966,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__max__iff__disj) ).
thf(20346,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3966]) ).
thf(1573,axiom,
( ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).
thf(10821,plain,
( ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573]) ).
thf(4519,axiom,
! [A: $i,B: $i] :
( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ c_Set_OCollect @ hAPP ) ) )
<=> ! [C: $i] :
~ ( C @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).
thf(22490,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( C @ ( A @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ c_Set_OCollect @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ c_Set_OCollect @ hAPP ) ) )
=> ! [C: $i] :
~ ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4519]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__Suc) ).
thf(5386,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(3131,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Groups_Ocomm__monoid__mult )
& ( C @ class_Groups_Ocomm__monoid__add ) )
=> ( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( A @ ( tc_Nat_Onat @ ( C @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).
thf(17039,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Groups_Ocomm__monoid__mult )
& ( C @ class_Groups_Ocomm__monoid__add ) )
=> ( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( A @ ( tc_Nat_Onat @ ( C @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3131]) ).
thf(1880,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__empty) ).
thf(12027,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1880]) ).
thf(3072,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oinsert) ).
thf(16814,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3072]) ).
thf(702,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_List_OtakeWhile ) ) )
= ( B @ ( E @ ( C @ c_List_OtakeWhile ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__tail) ).
thf(7412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_List_OtakeWhile ) ) )
= ( B @ ( E @ ( C @ c_List_OtakeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(4172,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( C @ ( E @ ( F @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( E = F )
| ( C @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( D @ c_List_Olexord ) @ ( B @ ( A @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( C @ ( D @ c_List_Olexord ) @ ( A @ ( B @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__linear) ).
thf(21180,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( C @ ( E @ ( F @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( E = F )
| ( C @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( D @ c_List_Olexord ) @ ( B @ ( A @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( C @ ( D @ c_List_Olexord ) @ ( A @ ( B @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4172]) ).
thf(926,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__1) ).
thf(8260,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(4530,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(22544,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4530]) ).
thf(806,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 )
= ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
thf(7816,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
= ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(1231,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( C @ ( B @ c_List_Ohd @ hAPP ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( A @ ( B @ c_List_Ohd @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__append) ).
thf(9417,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( C @ ( B @ c_List_Ohd @ hAPP ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( A @ ( B @ c_List_Ohd @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(2861,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Odistrib__lattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib2) ).
thf(15957,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Odistrib__lattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2861]) ).
thf(3396,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
thf(18061,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3396]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring__0 )
=> ( ( A @ ( B @ ( E @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( C @ ( E @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__right__distrib) ).
thf(5966,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring__0 )
=> ( ( A @ ( B @ ( E @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( C @ ( E @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(4349,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( C @ ( A @ ( B @ c_Finite__Set_Ocard @ ( D @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__SigmaI) ).
thf(21892,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( C @ ( A @ ( B @ c_Finite__Set_Ocard @ ( D @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4349]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__distrib) ).
thf(6390,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(4561,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I1_J) ).
thf(22647,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4561]) ).
thf(1007,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(8533,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(4686,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__remove) ).
thf(23121,plain,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4686]) ).
thf(2873,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__in) ).
thf(15997,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2873]) ).
thf(4719,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ( A
= ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
thf(23261,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A
= ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4719]) ).
thf(789,axiom,
! [A: $i,B: $i] :
~ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist__ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex1__simps_I1_J) ).
thf(7765,plain,
! [A: $i,B: $i] :
~ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist__ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(3251,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I8_J) ).
thf(17506,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3251]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__m1) ).
thf(4780,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4636,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
thf(22946,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4636]) ).
thf(3153,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Equiv__Relations_Ocongruent ) ) ) )
=> ( ( D @ ( A @ ( B @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruentD) ).
thf(17120,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Equiv__Relations_Ocongruent ) ) ) )
=> ( ( D @ ( A @ ( B @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3153]) ).
thf(3198,axiom,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I14_J) ).
thf(17294,plain,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3198]) ).
thf(2779,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( A @ ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__bij__betw__nat__finite) ).
thf(15625,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( A @ ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2779]) ).
thf(3066,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntE) ).
thf(16795,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3066]) ).
thf(1908,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(12130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1908]) ).
thf(567,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ ( D @ c_List_Olist_Olist__case ) ) ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
thf(6938,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ ( D @ c_List_Olist_Olist__case ) ) ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(2850,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Fun_Oid @ ( C @ ( C @ c_Fun_Obij__betw ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__id__iff) ).
thf(15910,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( A @ ( B @ ( C @ c_Fun_Oid @ ( C @ ( C @ c_Fun_Obij__betw ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ c_Fun_Oid @ ( C @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2850]) ).
thf(2007,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__dividend) ).
thf(12495,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2007]) ).
thf(2882,axiom,
! [A: $i] : ( c_Int_OInteg @ ( A @ ( c_Int_ORep__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ) ).
thf(16034,plain,
! [A: $i] : ( c_Int_OInteg @ ( A @ ( c_Int_ORep__Integ @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2882]) ).
thf(2679,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__single__insert) ).
thf(15260,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2679]) ).
thf(4781,plain,
! [A: $i] :
( ( ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(cnf,[status(esa)],[4780]) ).
thf(4782,plain,
! [A: $i] :
( ~ ( A @ class_Int_Onumber__ring )
| ( ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4781]) ).
thf(36065,plain,
! [A: $i] :
( ~ ( A @ class_Int_Onumber__ring )
| ( ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( A @ c_Int_Oring__1__class_Oof__int @ hAPP ) ) ) ),
inference(rewrite,[status(thm)],[4782,4775]) ).
thf(3968,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D != B )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I4_J) ).
thf(20353,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ! [E: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( E @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D
!= ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( D != B )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3968]) ).
thf(4088,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__def) ).
thf(20814,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4088]) ).
thf(892,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Wellfounded_Omlex__prod ) ) )
= ( C @ c_COMBI @ ( B @ ( C @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ ( C @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Wellfounded_Oless__than @ ( C @ ( tc_Nat_Onat @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__prod__def) ).
thf(8153,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Wellfounded_Omlex__prod ) ) )
= ( C @ c_COMBI @ ( B @ ( C @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ ( C @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Wellfounded_Oless__than @ ( C @ ( tc_Nat_Onat @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1934,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeastLessThan) ).
thf(12226,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1934]) ).
thf(1160,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).
thf(9141,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(2182,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).
thf(13178,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2182]) ).
thf(3376,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).
thf(17970,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3376]) ).
thf(2031,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
thf(12563,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2031]) ).
thf(4396,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(22070,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4396]) ).
thf(1148,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zminus__int) ).
thf(9078,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1066,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__takeWhile) ).
thf(8761,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(2537,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__iff) ).
thf(14695,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2537]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__eq) ).
thf(5389,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1255,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_Olist__size ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I1_J) ).
thf(9515,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_Olist__size ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(3111,axiom,
! [A: $i,B: $i] : ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__M__bounded__by__nat) ).
thf(16961,plain,
! [A: $i,B: $i] : ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3111]) ).
thf(1048,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
<=> ( ( B
= ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) ) )
& ( C
= ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__conv__conj) ).
thf(8666,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B
= ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) ) )
& ( C
= ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) ) ) )
=> ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ) )
& ( ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
=> ( ( B
= ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) ) )
& ( C
= ( A @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(2409,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost__int) ).
thf(14108,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2409]) ).
thf(1969,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olinorder__class_Osorted ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__single) ).
thf(12355,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olinorder__class_Osorted ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1969]) ).
thf(2522,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less) ).
thf(14626,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2522]) ).
thf(1824,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__length__takeWhile) ).
thf(11810,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1824]) ).
thf(1722,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).
thf(11412,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722]) ).
thf(3109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__equiv__class) ).
thf(16956,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3109]) ).
thf(871,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C @ ( F @ c_List_Olistrel1 ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = D ) )
| ( ( B = A )
& ( C @ ( F @ c_List_Olistrel1 ) @ ( D @ ( E @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( C @ ( F @ c_List_Olistrel1 ) @ ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__listrel1I) ).
thf(8075,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C @ ( F @ c_List_Olistrel1 ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = D ) )
| ( ( B = A )
& ( C @ ( F @ c_List_Olistrel1 ) @ ( D @ ( E @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( C @ ( F @ c_List_Olistrel1 ) @ ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(2416,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ c_List_Olist_ONil )
= ( A @ ( B @ ( C @ c_List_Oreplicate ) ) ) )
<=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__replicate) ).
thf(14133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ c_List_Olist_ONil )
= ( A @ ( B @ ( C @ c_List_Oreplicate ) ) ) ) )
& ( ( ( C @ c_List_Olist_ONil )
= ( A @ ( B @ ( C @ c_List_Oreplicate ) ) ) )
=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2416]) ).
thf(3736,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_OF__eq) ).
thf(19463,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3736]) ).
thf(619,axiom,
! [A: $i] :
( ( A @ c_Wellfounded_Omeasure )
= ( c_Wellfounded_Oless__than @ ( A @ ( tc_Nat_Onat @ c_Relation_Oinv__image ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measure__def) ).
thf(7131,plain,
! [A: $i] :
( ( A @ c_Wellfounded_Omeasure )
= ( c_Wellfounded_Oless__than @ ( A @ ( tc_Nat_Onat @ c_Relation_Oinv__image ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(1957,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__takeD) ).
thf(12302,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1957]) ).
thf(1239,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( D @ c_List_Oremove1 ) ) @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__map__remove1) ).
thf(9459,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( B @ ( A @ ( D @ c_List_Oremove1 ) ) @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(4716,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Relation_ORange ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty) ).
thf(23252,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Relation_ORange ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4716]) ).
thf(4008,axiom,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Complete__Lattice_OSup__class_OSup ) )
= ( B @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OAll @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__Inf) ).
thf(20487,plain,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Complete__Lattice_OSup__class_OSup ) )
= ( B @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OAll @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4008]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__drop) ).
thf(5258,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(3074,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__insert) ).
thf(16820,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3074]) ).
thf(1641,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Int_Ointrel @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_intrel__iff) ).
thf(11076,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( c_Int_Ointrel @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_Ointrel @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641]) ).
thf(841,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_Onat @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__number__of) ).
thf(7950,plain,
! [A: $i,B: $i] :
( ( ( c_Int_Onat @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_Onat @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(3253,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).
thf(17511,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3253]) ).
thf(956,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose ) )
= ( A @ ( D @ tc_List_Olist @ c_List_Olist_ONil @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_ONil @ ( D @ ( D @ tc_List_Olist @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Oconcat ) @ ( B @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose ) @ ( A @ ( D @ c_List_Olist_ONil @ ( D @ c_List_Olist_OCons @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_COMBK ) @ ( D @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist_ONil @ ( D @ ( D @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oconcat ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I3_J) ).
thf(8356,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose ) )
= ( A @ ( D @ tc_List_Olist @ c_List_Olist_ONil @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_ONil @ ( D @ ( D @ tc_List_Olist @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( D @ tc_List_Olist @ tc_List_Olist @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Oconcat ) @ ( B @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Otranspose ) @ ( A @ ( D @ c_List_Olist_ONil @ ( D @ c_List_Olist_OCons @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_COMBK ) @ ( D @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olist_ONil @ ( D @ ( D @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oconcat ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(2839,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI1) ).
thf(15869,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2839]) ).
thf(3626,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).
thf(19028,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3626]) ).
thf(1863,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__disjoint) ).
thf(11963,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1863]) ).
thf(4097,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= A ) )
=> ( ! [D: $i] :
( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( E @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) )
=> ( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__partition) ).
thf(20846,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= A ) )
=> ( ! [D: $i] :
( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( E @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) )
=> ( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Finite__Set_Ocard @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4097]) ).
thf(2405,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(14083,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2405]) ).
thf(4689,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientI) ).
thf(23128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4689]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( C @ c_List_Olist__ex ) ) )
<=> ( A @ ( B @ ( C @ c_List_Olist__ex ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__rev) ).
thf(4913,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Olist__ex ) ) )
=> ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( C @ c_List_Olist__ex ) ) ) )
& ( ( A @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( C @ c_List_Olist__ex ) ) )
=> ( A @ ( B @ ( C @ c_List_Olist__ex ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(4616,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( A @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( A @ ( B @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oinsert) ).
thf(22865,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( A @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( A @ ( B @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4616]) ).
thf(3914,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Groups_Oab__semigroup__mult )
=> ( ( E @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( E @ ( C @ ( D @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( E @ ( C @ ( D @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( G @ c_Groups_Otimes__class_Otimes @ ( D @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ ( C @ ( B @ ( F @ ( G @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( G @ c_Groups_Otimes__class_Otimes @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__reindex) ).
thf(20182,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Groups_Oab__semigroup__mult )
=> ( ( E @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( E @ ( C @ ( D @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( E @ ( C @ ( D @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( G @ c_Groups_Otimes__class_Otimes @ ( D @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ ( C @ ( B @ ( F @ ( G @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( G @ c_Groups_Otimes__class_Otimes @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3914]) ).
thf(1619,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
thf(10996,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619]) ).
thf(3145,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(17095,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3145]) ).
thf(2309,axiom,
! [A: $i] :
( ( A @ c_Relation_OId )
= ( A @ c_COMBI @ ( A @ ( A @ c_Product__Type_OPair ) @ ( A @ ( A @ tc_prod ) @ ( A @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( A @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ c_COMBB ) ) @ ( A @ ( A @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ ( A @ tc_prod ) @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ ( A @ tc_prod ) @ ( A @ tc_fun ) @ ( A @ ( A @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_OEx @ ( A @ ( A @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( A @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__def) ).
thf(13706,plain,
! [A: $i] :
( ( A @ c_Relation_OId )
= ( A @ c_COMBI @ ( A @ ( A @ c_Product__Type_OPair ) @ ( A @ ( A @ tc_prod ) @ ( A @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( A @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ c_COMBB ) ) @ ( A @ ( A @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ ( A @ tc_prod ) @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ ( A @ tc_prod ) @ ( A @ tc_fun ) @ ( A @ ( A @ tc_prod ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_OEx @ ( A @ ( A @ tc_prod ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( A @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2309]) ).
thf(3101,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__image) ).
thf(16931,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3101]) ).
thf(2968,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__fold__image) ).
thf(16397,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2968]) ).
thf(1701,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__drop) ).
thf(11337,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701]) ).
thf(405,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_List_Onth @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__le__listsum__nat) ).
thf(6230,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_List_Onth @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(3879,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
thf(20050,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3879]) ).
thf(3859,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ c_List_Oset @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip__rightD) ).
thf(19985,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ c_List_Oset @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3859]) ).
thf(3886,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( C @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold) ).
thf(20072,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( C @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3886]) ).
thf(3176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__less @ ( D @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omax__strict @ ( C @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omax__strict @ ( C @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__insertI) ).
thf(17227,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__less @ ( D @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omax__strict @ ( C @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omax__strict @ ( C @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3176]) ).
thf(2763,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__id) ).
thf(15576,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2763]) ).
thf(2419,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).
thf(14150,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2419]) ).
thf(3408,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
=> ( ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__mono__one__right) ).
thf(18115,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
=> ( ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3408]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( B = A )
<=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
thf(6818,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(1187,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(9234,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(1162,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ c_Int_Opred )
= ( A @ c_Int_Opred @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Bit0) ).
thf(9147,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 @ c_Int_Opred )
= ( A @ c_Int_Opred @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(2381,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
thf(13959,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2381]) ).
thf(4222,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(21369,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4222]) ).
thf(2124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__upper) ).
thf(12915,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2124]) ).
thf(2912,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( D
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons_H) ).
thf(16161,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( D
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2912]) ).
thf(492,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
thf(6607,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1524,axiom,
! [A: $i,B: $i] :
( ( B @ c_Int_OBit1 )
!= ( A @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).
thf(10605,plain,
! [A: $i,B: $i] :
( ( B @ c_Int_OBit1 )
!= ( A @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524]) ).
thf(4659,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Pow__eq) ).
thf(23029,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_OPow @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4659]) ).
thf(4144,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oid @ ( A @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__id) ).
thf(21061,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oid @ ( A @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4144]) ).
thf(3200,axiom,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ ( B @ ( B @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fold__sup) ).
thf(17301,plain,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ ( B @ ( B @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3200]) ).
thf(686,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
thf(7359,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(506,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I8_J) ).
thf(6689,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(2064,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__nat__iff) ).
thf(12698,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2064]) ).
thf(3629,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Ocommute) ).
thf(19041,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3629]) ).
thf(4101,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(20898,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4101]) ).
thf(4190,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ~ ! [D: $i] : ( B @ ( D @ ( A @ hAPP ) @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( A @ hAPP ) @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__no__infinite__down__chainE) ).
thf(21264,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ~ ! [D: $i] : ( B @ ( D @ ( A @ hAPP ) @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( A @ hAPP ) @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4190]) ).
thf(3780,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterE) ).
thf(19654,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3780]) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__square) ).
thf(6030,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(3698,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( ( C @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Owf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pair__lemma) ).
thf(19307,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( ( C @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Owf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3698]) ).
thf(2054,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).
thf(12662,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2054]) ).
thf(2404,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ! [F: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__transfer) ).
thf(14079,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ! [F: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2404]) ).
thf(4138,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__upper) ).
thf(21036,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4138]) ).
thf(1442,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(10225,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Divides_Odivmod__int ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__int__def) ).
thf(5132,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Divides_Odivmod__int ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1563,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Orev @ hAPP ) @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__update) ).
thf(10789,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Orev @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Orev @ hAPP ) @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563]) ).
thf(4555,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__wf) ).
thf(22633,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4555]) ).
thf(3646,axiom,
( ( tc_Nat_Onat @ c_Lattices_Osemilattice__sup__class_Osup )
= ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__nat__def) ).
thf(19096,plain,
( ( tc_Nat_Onat @ c_Lattices_Osemilattice__sup__class_Osup )
= ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3646]) ).
thf(19097,plain,
( ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax )
= ( tc_Nat_Onat @ c_Lattices_Osemilattice__sup__class_Osup ) ),
inference(lifteq,[status(thm)],[19096]) ).
thf(2078,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient) ).
thf(12743,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2078]) ).
thf(937,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__listsum__map) ).
thf(8292,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(3388,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(18034,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3388]) ).
thf(4601,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(22808,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4601]) ).
thf(1761,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
<=> ( ! [F: $i] :
( ( A @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( F @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__def) ).
thf(11585,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ! [F: $i] :
( ( A @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( F @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
=> ( ! [F: $i] :
( ( A @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( F @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1761]) ).
thf(2704,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( B = A )
<=> ( ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I3_J) ).
thf(15341,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( ( ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2704]) ).
thf(3574,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oidem) ).
thf(18818,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3574]) ).
thf(1459,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__minus1__right) ).
thf(10352,plain,
! [A: $i] :
( ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(2494,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(14503,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2494]) ).
thf(1975,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).
thf(12370,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1975]) ).
thf(3611,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD) ).
thf(18950,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3611]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( C @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__nth) ).
thf(7012,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( C @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(2101,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(12815,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2101]) ).
thf(1490,axiom,
! [A: $i] :
( ( A @ ( c_Int_ORep__Integ @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inverse) ).
thf(10468,plain,
! [A: $i] :
( ( A @ ( c_Int_ORep__Integ @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490]) ).
thf(2660,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
thf(15191,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2660]) ).
thf(4607,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_thin) ).
thf(22830,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4607]) ).
thf(3643,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).
thf(19087,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3643]) ).
thf(3788,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(19686,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3788]) ).
thf(3792,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olex ) )
= ( A @ ( B @ c_List_Olexn ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lex__def) ).
thf(19697,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olex ) )
= ( A @ ( B @ c_List_Olexn ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_Nat_Onat @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3792]) ).
thf(1101,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_OnegDivAlg ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__div__mod) ).
thf(8912,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_OnegDivAlg ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(1451,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append2) ).
thf(10325,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(3667,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__product) ).
thf(19175,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3667]) ).
thf(2886,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(16053,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2886]) ).
thf(2519,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Int) ).
thf(14618,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2519]) ).
thf(3374,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupt ) )
= ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__rec) ).
thf(17960,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupt ) )
= ( tc_Nat_Onat @ c_List_Olist_ONil ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupt ) )
= ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3374]) ).
thf(3296,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( A @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( B @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__subset) ).
thf(17672,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( A @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( B @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3296]) ).
thf(26615,plain,
( ( ( c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8089,13069]) ).
thf(26616,plain,
( ( c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[26615]) ).
thf(26632,plain,
( ( c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) )
!= c_fTrue ),
inference(simp,[status(thm)],[26616]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( B @ ( C @ c_List_Osublist ) ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Osublist ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__in__sublist) ).
thf(5813,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( B @ ( C @ c_List_Osublist ) ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Osublist ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(4200,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
<=> ( ( A
= ( C @ c_List_Olist_ONil ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__eq__Nil) ).
thf(21295,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A
= ( C @ c_List_Olist_ONil ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
=> ( ( A
= ( C @ c_List_Olist_ONil ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4200]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ tc_prod ) @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__zip) ).
thf(8606,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ tc_prod ) @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(1941,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty) ).
thf(12245,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1941]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__diff) ).
thf(5368,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(4711,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product__singleton) ).
thf(23233,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4711]) ).
thf(2737,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less__Suc) ).
thf(15476,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2737]) ).
thf(4465,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Odistrib__lattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
thf(22299,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Odistrib__lattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4465]) ).
thf(2953,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(16337,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2953]) ).
thf(3640,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Big__Operators_Ocomm__monoid__big ) ) ) ) )
=> ( ~ ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).
thf(19077,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Big__Operators_Ocomm__monoid__big ) ) ) ) )
=> ( ~ ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3640]) ).
thf(1061,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__acyclic__wf__converse) ).
thf(8722,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Lazy__Sequence_Osmall__lazy_H__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Lazy__Sequence_Osmall__lazy_H__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( E @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( E @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__lazy_H_Opinduct) ).
thf(6494,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Lazy__Sequence_Osmall__lazy_H__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( c_Lazy__Sequence_Osmall__lazy_H__rel @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( E @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( E @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1040,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).
thf(8634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(1476,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
thf(10411,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(4681,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).
thf(23109,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4681]) ).
thf(2222,axiom,
! [A: $i] :
( ( A @ c_Int_Opred )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__def) ).
thf(13318,plain,
! [A: $i] :
( ( A @ c_Int_Opred )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2222]) ).
thf(770,axiom,
! [A: $i] :
( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Opred ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min) ).
thf(7700,plain,
! [A: $i] :
( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_Int_Opred ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1429,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
thf(10182,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(2162,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oassoc) ).
thf(13080,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2162]) ).
thf(3758,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Nitpick_Ocard_H ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Nitpick_Ocard_H ) )
= ( B @ c_List_Odistinct @ ( A @ ( B @ c_List_Oset @ ( c_fequal @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Hilbert__Choice_OEps ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ocard_H__def) ).
thf(19554,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Nitpick_Ocard_H ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Nitpick_Ocard_H ) )
= ( B @ c_List_Odistinct @ ( A @ ( B @ c_List_Oset @ ( c_fequal @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( B @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ c_Hilbert__Choice_OEps ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3758]) ).
thf(3790,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( E @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
thf(19692,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( E @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3790]) ).
thf(1784,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring__0 )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( B @ ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__mult__const) ).
thf(11663,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring__0 )
=> ( ( A @ ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( B @ ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784]) ).
thf(2265,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc) ).
thf(13502,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2265]) ).
thf(2314,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I7_J) ).
thf(13721,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2314]) ).
thf(104,axiom,
( c_Divides_OnegateSnd
= ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oapsnd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negateSnd__def) ).
thf(5087,plain,
( c_Divides_OnegateSnd
= ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oapsnd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__minus) ).
thf(5243,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__0__0) ).
thf(6618,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(3234,axiom,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
thf(17434,plain,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3234]) ).
thf(4683,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__DSequence_Opos__union ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ c_Lazy__Sequence_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__union__def) ).
thf(23114,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__DSequence_Opos__union ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ c_Lazy__Sequence_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4683]) ).
thf(2767,axiom,
tc_Nat_Onat @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
thf(15589,plain,
tc_Nat_Onat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2767]) ).
thf(1903,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).
thf(12113,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1903]) ).
thf(4288,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
thf(21648,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4288]) ).
thf(3166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__D) ).
thf(17195,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3166]) ).
thf(872,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Obutlast ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__conv__take) ).
thf(8083,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Obutlast ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).
thf(8716,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ c_Relation_Oconverse ) @ hAPP ) @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(3427,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq) ).
thf(18217,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3427]) ).
thf(2318,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) )
<=> ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__many__eq) ).
thf(13733,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) ) )
& ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Olinorder__class_Osorted ) )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2318]) ).
thf(3263,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
thf(17540,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3263]) ).
thf(1034,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality_H) ).
thf(8617,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(1624,axiom,
! [A: $i,B: $i] :
( ( B @ c_Int_OBit0 )
!= ( A @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).
thf(11013,plain,
! [A: $i,B: $i] :
( ( B @ c_Int_OBit0 )
!= ( A @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624]) ).
thf(3984,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( D @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__subsetI) ).
thf(20414,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( D @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3984]) ).
thf(3709,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__diff) ).
thf(19346,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3709]) ).
thf(3275,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( D != C ) )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( G @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( A @ ( G @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__E) ).
thf(17593,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( D != C ) )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( G @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( A @ ( G @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3275]) ).
thf(843,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__def) ).
thf(7959,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(3500,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI) ).
thf(18501,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3500]) ).
thf(4020,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__empty__induct) ).
thf(20523,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4020]) ).
thf(1308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(9736,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(919,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(8240,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(3906,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI1) ).
thf(20150,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__sup )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3906]) ).
thf(1079,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Bit0) ).
thf(8805,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(3622,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) )
<=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( A @ ( D @ ( E @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).
thf(18996,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( A @ ( D @ ( E @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) ) )
& ( ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) )
=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( A @ ( D @ ( E @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3622]) ).
thf(1404,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__filter) ).
thf(10077,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_COMBI @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__even) ).
thf(5600,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_COMBI @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(830,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).
thf(7912,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(2140,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupt ) )
= ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__conv__Cons) ).
thf(12976,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oupt ) )
= ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) @ ( B @ ( tc_Nat_Onat @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2140]) ).
thf(1849,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__remainder) ).
thf(11918,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1849]) ).
thf(2728,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__sym) ).
thf(15437,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2728]) ).
thf(4121,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert) ).
thf(20970,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4121]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( D @ ( A @ ( E @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update__neq) ).
thf(6354,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( D @ ( A @ ( E @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1472,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__commute) ).
thf(10400,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(3719,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff) ).
thf(19388,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3719]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__le__iff) ).
thf(4745,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1689,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(11287,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1689]) ).
thf(3507,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( B @ ( E @ c_Quotient_OBabs ) ) ) @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Babs__def) ).
thf(18518,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( B @ ( E @ c_Quotient_OBabs ) ) ) @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3507]) ).
thf(4649,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Diff) ).
thf(22990,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4649]) ).
thf(4446,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I2_J) ).
thf(22230,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4446]) ).
thf(2329,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__subset__Int) ).
thf(13780,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2329]) ).
thf(2507,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).
thf(14560,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2507]) ).
thf(4089,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ! [D: $i] :
( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__disjoint) ).
thf(20817,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ! [D: $i] :
( ( B @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4089]) ).
thf(416,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OposDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg) ).
thf(6257,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OposDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Osnd ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(4178,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).
thf(21208,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( C @ c_COMBB ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ c_COMBS ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_HOL_OEx @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4178]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__sum) ).
thf(5963,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(4244,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I6_J) ).
thf(21487,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4244]) ).
thf(2575,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanAtMost__int) ).
thf(14845,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2575]) ).
thf(4370,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(21977,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4370]) ).
thf(1302,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_List_Otl @ hAPP ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__tl) ).
thf(9718,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_List_Otl @ hAPP ) @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(1670,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(11210,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670]) ).
thf(1834,axiom,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(11850,plain,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1834]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1__strict )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(7256,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1__strict )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(3600,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_COMBB ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ ( A @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ tc_prod ) @ c_Set_OCollect @ ( A @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ tc_fun ) @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__graph) ).
thf(18911,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_COMBB ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ ( A @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ tc_prod ) @ c_Set_OCollect @ ( A @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ tc_fun ) @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3600]) ).
thf(4129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) )
=> ( ( B @ ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__1) ).
thf(21011,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) )
=> ( ( B @ ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4129]) ).
thf(4142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ ( D @ c_Relation_ORange ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
thf(21049,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Relation_ORange ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_Relation_ORange ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4142]) ).
thf(4050,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I16_J) ).
thf(20644,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4050]) ).
thf(2334,axiom,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) )
= A )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc) ).
thf(13793,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) )
= A )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2334]) ).
thf(4040,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).
thf(20604,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4040]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__add )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__absorb0) ).
thf(5162,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__add )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(546,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(6854,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(7187,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1 )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(7266,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1 )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(1295,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus__even) ).
thf(9701,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(3614,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( D @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__image__Collect__eq) ).
thf(18960,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( D @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Set_OCollect @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3614]) ).
thf(3392,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Otl @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__replicate) ).
thf(18051,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( B @ c_List_Otl @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3392]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit0) ).
thf(5532,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(3723,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( G @ ( H @ ( I @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( D @ ( E @ ( F @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( B @ ( D @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ ( I @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
=> ( ( E @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( I @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( I @ c_Equiv__Relations_Ocongruent ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2__implies__congruent__UN) ).
thf(19403,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( G @ ( H @ ( I @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( D @ ( E @ ( F @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( B @ ( D @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ ( I @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
=> ( ( E @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ ( I @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( I @ c_Equiv__Relations_Ocongruent ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3723]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).
thf(6181,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(3280,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).
thf(17621,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3280]) ).
thf(3989,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__lower) ).
thf(20425,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3989]) ).
thf(3377,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).
thf(17973,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3377]) ).
thf(1253,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incr__lemma) ).
thf(9510,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(1921,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__le__divisor) ).
thf(12176,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1921]) ).
thf(2038,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
thf(12588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2038]) ).
thf(2623,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(15052,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2623]) ).
thf(967,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Equiv__Relations_Opart__equivp ) )
=> ( ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__symp) ).
thf(8388,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Equiv__Relations_Opart__equivp ) )
=> ( ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(1362,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( A @ ( C @ ( B @ ( D @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__inv__image) ).
thf(9906,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( A @ ( C @ ( B @ ( D @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(2789,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
thf(15667,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2789]) ).
thf(4104,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I9_J) ).
thf(20910,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4104]) ).
thf(2915,axiom,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__int__def) ).
thf(16180,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2915]) ).
thf(3741,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(19489,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3741]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
<=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__iff__number__of) ).
thf(7715,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(3245,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) )
= A )
<=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__id__conv) ).
thf(17474,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) )
= A ) )
& ( ( ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) )
= A )
=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3245]) ).
thf(908,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).
thf(8203,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1044,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
<=> ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
thf(8649,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(4498,axiom,
! [A: $i] : ( A @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).
thf(22408,plain,
! [A: $i] : ( A @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4498]) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).
thf(6018,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(4313,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__INT) ).
thf(21745,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4313]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( ( ~ ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__relI) ).
thf(7312,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( ( ~ ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(1549,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oupt ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__Suc__upt) ).
thf(10738,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oupt ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).
thf(4551,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).
thf(22615,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4551]) ).
thf(851,axiom,
tc_Int_Oint @ class_Rings_Olinordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(7979,plain,
tc_Int_Oint @ class_Rings_Olinordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(3478,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib1) ).
thf(18409,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3478]) ).
thf(3051,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(16739,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3051]) ).
thf(784,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( B @ c_List_Oremove1 ) ) )
= ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__filter__not) ).
thf(7747,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( B @ c_List_Oremove1 ) ) )
= ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1826,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= B )
<=> ( ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__same__conv) ).
thf(11815,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= A )
=> ( ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= B ) )
& ( ( ( A @ ( D @ ( B @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= B )
=> ( ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1826]) ).
thf(2325,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( D @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
thf(13761,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( D @ ( D @ c_Relation_ODomain ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C = A )
=> ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2325]) ).
thf(3624,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(19014,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3624]) ).
thf(2977,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(16438,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2977]) ).
thf(4273,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power__div__base) ).
thf(21589,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4273]) ).
thf(2599,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oin__idem) ).
thf(14928,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OInf__fin ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2599]) ).
thf(1183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( E @ ( A @ ( B @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(9223,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( E @ ( A @ ( B @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(4673,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Enum_Oenum )
& ( B @ class_Enum_Oenum ) )
=> ( A @ ( B @ tc_fun ) @ class_Enum_Oenum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Enum_Oenum) ).
thf(23077,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Enum_Oenum )
& ( B @ class_Enum_Oenum ) )
=> ( A @ ( B @ tc_fun ) @ class_Enum_Oenum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4673]) ).
thf(4079,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__int__split) ).
thf(20768,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4079]) ).
thf(4242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Owf ) )
<=> ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Owf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__insert) ).
thf(21472,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Owf ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Owf ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Owf ) )
=> ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Owf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4242]) ).
thf(272,axiom,
! [A: $i] :
( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).
thf(5699,plain,
! [A: $i] :
( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(4579,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty) ).
thf(22720,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4579]) ).
thf(1731,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).
thf(11454,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731]) ).
thf(3158,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ? [C: $i] : ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oneutral) ).
thf(17153,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ? [C: $i] : ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3158]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acyclic) ).
thf(7157,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(1371,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_COMBI @ ( C @ c_COMBI @ ( B @ ( B @ ( C @ ( C @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__ident) ).
thf(9955,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_COMBI @ ( C @ c_COMBI @ ( B @ ( B @ ( C @ ( C @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OposDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( B @ c_Divides_OnegDivAlg ) ) ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) ) ) )
& ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( B @ c_Divides_OposDivAlg ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__def) ).
thf(5549,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OposDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( B @ c_Divides_OnegDivAlg ) ) ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OnegDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) ) ) )
& ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( B @ c_Divides_OposDivAlg ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(3506,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__upt) ).
thf(18515,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3506]) ).
thf(3462,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(18337,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3462]) ).
thf(971,axiom,
! [A: $i,B: $i] :
( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ c_Nitpick_Onorm__frac ) )
= ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Nitpick_Oint__gcd @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ c_Nitpick_Onorm__frac ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nitpick_Onorm__frac ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Nitpick_Onorm__frac ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Osimps) ).
thf(8399,plain,
! [A: $i,B: $i] :
( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ c_Nitpick_Onorm__frac ) )
= ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Nitpick_Oint__gcd @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ c_Nitpick_Onorm__frac ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nitpick_Onorm__frac ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Nitpick_Onorm__frac ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(1660,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Orotate ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( C @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__rotate__conv__nth) ).
thf(11172,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Orotate ) @ hAPP ) @ ( B @ c_List_Ohd @ hAPP ) )
= ( C @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660]) ).
thf(2707,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__top )
=> ( ( A @ ( B @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__top__left) ).
thf(15362,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__top )
=> ( ( A @ ( B @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2707]) ).
thf(2043,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
thf(12620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2043]) ).
thf(4128,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fFalse @ ( tc_HOL_Obool @ c_Nat_Onat_Onat__case ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
thf(21005,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fFalse @ ( tc_HOL_Obool @ c_Nat_Onat_Onat__case ) ) ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fFalse @ ( tc_HOL_Obool @ c_Nat_Onat_Onat__case ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4128]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( B @ ( C @ ( c_fequal @ ( A @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__eq) ).
thf(5568,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( c_fequal @ ( A @ ( A @ c_List_Olist__all2 ) ) ) ) )
=> ( C = B ) )
& ( ( C = B )
=> ( B @ ( C @ ( c_fequal @ ( A @ ( A @ c_List_Olist__all2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(3159,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] :
( ! [F: $i] :
( ( A
= ( F @ ( B @ hAPP ) ) )
=> ( F = E ) )
& ( A
= ( E @ ( B @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
thf(17159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( ? [E: $i] :
( ! [F: $i] :
( ( A
= ( F @ ( B @ hAPP ) ) )
=> ( F = E ) )
& ( A
= ( E @ ( B @ hAPP ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ! [F: $i] :
( ( A
= ( F @ ( B @ hAPP ) ) )
=> ( F = E ) )
& ( A
= ( E @ ( B @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3159]) ).
thf(1996,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).
thf(12448,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ ( C @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1996]) ).
thf(3715,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_OwfP ) )
<=> ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__def) ).
thf(19371,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_OwfP ) ) )
& ( ( A @ ( B @ c_Wellfounded_OwfP ) )
=> ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3715]) ).
thf(3121,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__iff__sup) ).
thf(16993,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3121]) ).
thf(1157,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Divides_OposDivAlg ) )
= ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Divides_OposDivAlg ) @ ( B @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Divides_OposDivAlg ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn) ).
thf(9130,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Divides_OposDivAlg ) )
= ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Divides_OposDivAlg ) @ ( B @ c_Divides_Oadjust @ hAPP ) ) ) )
& ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Divides_OposDivAlg ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(3151,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ~ ( B @ ( A @ ( A @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__refl) ).
thf(17116,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ~ ( B @ ( A @ ( A @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3151]) ).
thf(4588,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
thf(22756,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4588]) ).
thf(3645,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
thf(19092,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3645]) ).
thf(1897,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).
thf(12093,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1897]) ).
thf(1914,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ c_member @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_OwfP ) )
<=> ( A @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__wf__eq) ).
thf(12152,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ c_member @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_OwfP ) ) )
& ( ( A @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ c_member @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_OwfP ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1914]) ).
thf(414,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Omeasures ) @ ( B @ c_Wellfounded_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measures) ).
thf(6252,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Omeasures ) @ ( B @ c_Wellfounded_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Orotate1 @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__length01) ).
thf(5144,plain,
! [A: $i,B: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Orotate1 @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(728,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
thf(7530,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) ) ) )
& ( ( ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(2340,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( B @ ( B @ c_Relation_ORange ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__range) ).
thf(13816,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( B @ ( B @ c_Relation_ORange ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2340]) ).
thf(2865,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Relation_Orefl__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__rtrancl) ).
thf(15977,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Relation_Orefl__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2865]) ).
thf(3352,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( D @ ( B @ ( C @ ( G @ c_Fun_Obij__betw ) ) ) ) )
<=> ( A @ ( E @ ( F @ ( B @ ( H @ ( C @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( H @ c_Fun_Obij__betw ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__comp__iff) ).
thf(17872,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( ( A @ ( E @ ( F @ ( B @ ( H @ ( C @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( H @ c_Fun_Obij__betw ) ) ) ) )
=> ( A @ ( D @ ( B @ ( C @ ( G @ c_Fun_Obij__betw ) ) ) ) ) )
& ( ( A @ ( D @ ( B @ ( C @ ( G @ c_Fun_Obij__betw ) ) ) ) )
=> ( A @ ( E @ ( F @ ( B @ ( H @ ( C @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( H @ c_Fun_Obij__betw ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3352]) ).
thf(3865,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__minus__filter__out) ).
thf(20006,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Ofilter ) @ hAPP ) @ ( C @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3865]) ).
thf(3785,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Osublist ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__sublist) ).
thf(19669,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Osublist ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3785]) ).
thf(2379,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__antimono) ).
thf(13954,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2379]) ).
thf(4582,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Set_Oinsert @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I5_J) ).
thf(22739,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Set_Oinsert @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4582]) ).
thf(4500,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
thf(22413,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4500]) ).
thf(1181,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(9211,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(1601,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of__Suc) ).
thf(10924,plain,
! [A: $i,B: $i] :
( ( ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601]) ).
thf(1639,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(11071,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639]) ).
thf(2114,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
<=> ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(12851,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2114]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_List_Orev @ hAPP ) )
= A )
<=> ( B
= ( A @ ( C @ c_List_Orev @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__swap) ).
thf(5517,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B
= ( A @ ( C @ c_List_Orev @ hAPP ) ) )
=> ( ( B @ ( C @ c_List_Orev @ hAPP ) )
= A ) )
& ( ( ( B @ ( C @ c_List_Orev @ hAPP ) )
= A )
=> ( B
= ( A @ ( C @ c_List_Orev @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(2067,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Fun_Oid @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__def) ).
thf(12711,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Fun_Oid @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2067]) ).
thf(4334,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__0) ).
thf(21840,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4334]) ).
thf(2432,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(14234,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2432]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Orev @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
<=> ( A @ ( D @ c_List_Orev @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__rev1) ).
thf(5672,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( D @ c_List_Orev @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
=> ( A @ ( B @ ( E @ c_List_Orev @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) ) )
& ( ( A @ ( B @ ( E @ c_List_Orev @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) )
=> ( A @ ( D @ c_List_Orev @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__all2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1215,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Suc__Cons) ).
thf(9350,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(4701,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).
thf(23200,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4701]) ).
thf(4447,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Opos__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Osingle @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
thf(22239,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Opos__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Osingle @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4447]) ).
thf(1411,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Osemilattice__inf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
thf(10109,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Osemilattice__inf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(4611,axiom,
tc_HOL_Obool @ class_Groups_Ouminus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
thf(22844,plain,
tc_HOL_Obool @ class_Groups_Ouminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4611]) ).
thf(110,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).
thf(5128,plain,
tc_Code__Numeral_Ocode__numeral @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1847,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) @ ( A @ ( tc_Int_Oint @ c_Lazy__Sequence_Osingle @ hAPP ) @ ( tc_Int_Oint @ c_Lazy__Sequence_Oappend ) ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) )
= ( tc_Int_Oint @ c_Lazy__Sequence_Oempty ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__lazy_H_Osimps) ).
thf(11904,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) @ ( A @ ( tc_Int_Oint @ c_Lazy__Sequence_Osingle @ hAPP ) @ ( tc_Int_Oint @ c_Lazy__Sequence_Oappend ) ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Lazy__Sequence_Osmall__lazy_H ) )
= ( tc_Int_Oint @ c_Lazy__Sequence_Oempty ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1847]) ).
thf(700,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) )
= ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__upt) ).
thf(7406,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) )
= ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(4152,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infE) ).
thf(21100,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4152]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Divides_Odivmod__nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).
thf(5196,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Divides_Odivmod__nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(4045,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
& ( E @ class_Groups_Ocomm__monoid__add ) )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__strict__mono) ).
thf(20622,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
& ( E @ class_Groups_Ocomm__monoid__add ) )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4045]) ).
thf(4269,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__0) ).
thf(21574,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4269]) ).
thf(1327,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
thf(9787,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(1461,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
thf(10357,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(1168,axiom,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__num__one) ).
thf(9162,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(3112,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_OwfP ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_OwfP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__subset) ).
thf(16963,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_OwfP ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_OwfP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3112]) ).
thf(4575,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).
thf(22707,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4575]) ).
thf(2239,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(13389,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2239]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( E @ ( F @ ( G @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
=> ( ( D @ ( G @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__eq__imp__length__eq) ).
thf(6462,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( E @ ( F @ ( G @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
=> ( ( D @ ( G @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ c_List_Oremdups ) @ ( B @ ( C @ ( D @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ ( E @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).
thf(6499,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ c_List_Oremdups ) @ ( B @ ( C @ ( D @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ ( E @ ( D @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(3260,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__mono) ).
thf(17528,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3260]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2) ).
thf(4927,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(3841,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Equiv__Relations_Oequiv ) ) )
<=> ( A @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ c_member @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Equiv__Relations_Oequivp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__equiv) ).
thf(19901,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ c_member @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Equiv__Relations_Oequivp ) )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Equiv__Relations_Oequiv ) ) ) )
& ( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Equiv__Relations_Oequiv ) ) )
=> ( A @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ c_member @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Equiv__Relations_Oequivp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3841]) ).
thf(2745,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__0) ).
thf(15508,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2745]) ).
thf(3440,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__0) ).
thf(18263,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3440]) ).
thf(1920,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__le__iff) ).
thf(12171,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1920]) ).
thf(1906,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMostSuc__conv) ).
thf(12125,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1906]) ).
thf(3194,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Equiv__Relations_Oquotient @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__diff1) ).
thf(17279,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Equiv__Relations_Oquotient @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3194]) ).
thf(3603,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olists ) @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists_ONil) ).
thf(18922,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olists ) @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3603]) ).
thf(3778,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( G @ class_Orderings_Oord )
& ( H @ class_Groups_Ocomm__monoid__add ) )
=> ( ( F = E )
=> ( ( D = C )
=> ( ! [I: $i] :
( ( I @ ( E @ ( G @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( I @ ( G @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( B @ hAPP ) )
= ( I @ ( A @ hAPP ) ) ) ) )
=> ( ( D @ ( F @ ( G @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( H @ ( G @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ ( G @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( H @ ( G @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__ivl__cong) ).
thf(19637,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( G @ class_Orderings_Oord )
& ( H @ class_Groups_Ocomm__monoid__add ) )
=> ( ( F = E )
=> ( ( D = C )
=> ( ! [I: $i] :
( ( I @ ( E @ ( G @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( I @ ( G @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( B @ hAPP ) )
= ( I @ ( A @ hAPP ) ) ) ) )
=> ( ( D @ ( F @ ( G @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( H @ ( G @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ ( G @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( A @ ( H @ ( G @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3778]) ).
thf(1205,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__code__numeral__def) ).
thf(9321,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(2785,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olist_ONil @ ( B @ ( D @ c_List_Olist_OCons @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oconcat ) )
= ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__map__singleton) ).
thf(15652,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olist_ONil @ ( B @ ( D @ c_List_Olist_OCons @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Oconcat ) )
= ( A @ ( B @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2785]) ).
thf(4724,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Big__Operators_Olattice__class_OSup__fin ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Osingleton) ).
thf(23293,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Big__Operators_Olattice__class_OSup__fin ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4724]) ).
thf(1583,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Olinorder__class_Osorted ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__upto) ).
thf(10853,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Olinorder__class_Osorted ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) )
!= ( C @ c_List_Olist_ONil ) )
=> ~ ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Ohd @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__dropWhile) ).
thf(9262,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) )
!= ( C @ c_List_Olist_ONil ) )
=> ~ ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Ohd @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(2694,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( B @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__nondisjoint) ).
thf(15300,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( F @ c_Relation_OImage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( B @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2694]) ).
thf(2226,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Odistrib) ).
thf(13328,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2226]) ).
thf(1974,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Hilbert__Choice_OEps ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__trivial) ).
thf(12367,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Hilbert__Choice_OEps ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1974]) ).
thf(3881,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__zero) ).
thf(20054,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3881]) ).
thf(3163,axiom,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( B @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ ( B @ ( B @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__set__fold) ).
thf(17184,plain,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( B @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ ( B @ ( B @ c_List_Ofoldl ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3163]) ).
thf(2938,axiom,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
<=> ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_enum__ex) ).
thf(16271,plain,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2938]) ).
thf(1807,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__take__drop__id) ).
thf(11744,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1807]) ).
thf(1658,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ ( B @ c_List_Otl @ hAPP ) @ ( A @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_List_Ohd @ hAPP ) @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc) ).
thf(11167,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ ( B @ c_List_Otl @ hAPP ) @ ( A @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_List_Ohd @ hAPP ) @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1658]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Product__Type_Ofst ) @ ( D @ ( B @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__fst__zip) ).
thf(6703,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Product__Type_Ofst ) @ ( D @ ( B @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(3179,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).
thf(17233,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3179]) ).
thf(3492,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( ( D @ ( B @ hAPP ) )
= A )
& ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat0__intermed__int__val) ).
thf(18470,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( ( D @ ( B @ hAPP ) )
= A )
& ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3492]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
thf(6924,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(3340,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc2) ).
thf(17829,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3340]) ).
thf(4594,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__eq__UN) ).
thf(22780,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4594]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Osym ) )
=> ( A @ ( B @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__sym) ).
thf(5852,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Osym ) )
=> ( A @ ( B @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1980,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Relation_Osingle__valued ) ) )
=> ( ( D @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedD) ).
thf(12391,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Relation_Osingle__valued ) ) )
=> ( ( D @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1980]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ c_Fun_Oid @ ( A @ ( B @ ( B @ c_Product__Type_Oapsnd ) ) ) )
= ( B @ ( A @ tc_prod ) @ c_Fun_Oid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__id) ).
thf(4880,plain,
! [A: $i,B: $i] :
( ( B @ c_Fun_Oid @ ( A @ ( B @ ( B @ c_Product__Type_Oapsnd ) ) ) )
= ( B @ ( A @ tc_prod ) @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1578,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Osym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Un__converse) ).
thf(10838,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Osym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578]) ).
thf(4011,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
thf(20495,plain,
! [A: $i] :
( ( ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4011]) ).
thf(3856,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( A @ ( G @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F = G ) ) )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).
thf(19970,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( A @ ( G @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F = G ) ) )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3856]) ).
thf(4167,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
<=> ~ ? [C: $i] :
! [D: $i] : ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( C @ hAPP ) @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).
thf(21157,plain,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
! [D: $i] : ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( C @ hAPP ) @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) )
& ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ~ ? [C: $i] :
! [D: $i] : ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( C @ hAPP ) @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4167]) ).
thf(644,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).
thf(7216,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(4645,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D1) ).
thf(22978,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4645]) ).
thf(2425,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ! [E: $i] :
( ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E != F )
=> ! [G: $i] :
( ( E @ ( G @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( G @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( A @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) )
=> ( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__UNION__zero) ).
thf(14176,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ! [E: $i] :
( ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E != F )
=> ! [G: $i] :
( ( E @ ( G @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( G @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( A @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) )
=> ( ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2425]) ).
thf(3425,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Oreplicate ) ) )
= ( C @ c_List_Olist_ONil ) )
<=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__empty) ).
thf(18206,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_List_Oreplicate ) ) )
= ( C @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ ( C @ c_List_Oreplicate ) ) )
= ( C @ c_List_Olist_ONil ) )
=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3425]) ).
thf(2917,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__left__commute) ).
thf(16186,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2917]) ).
thf(607,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power2) ).
thf(7081,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(9346,plain,
( ( tc_Code__Numeral_Ocode__numeral @ c_Nat_Osemiring__1__class_Oof__nat )
= c_Code__Numeral_Oof__nat ),
inference(lifteq,[status(thm)],[9345]) ).
thf(4415,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__binary) ).
thf(22130,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4415]) ).
thf(2710,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistrelp ) ) ) )
<=> ( C @ ( D @ c_List_Olistrel ) @ ( A @ ( B @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp__listrel__eq) ).
thf(15371,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_List_Olistrel ) @ ( A @ ( B @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistrelp ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistrelp ) ) ) )
=> ( C @ ( D @ c_List_Olistrel ) @ ( A @ ( B @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2710]) ).
thf(4175,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__1__Cons) ).
thf(21199,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4175]) ).
thf(2606,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3div ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3div ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z3div__def) ).
thf(14952,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3div ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3div ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2606]) ).
thf(366,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Odistinct @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__upto) ).
thf(6055,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Odistinct @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(4203,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__max__iff__disj) ).
thf(21312,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4203]) ).
thf(1517,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Orev @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( ( B @ ( C @ ( A @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Ofilter ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_OtakeWhile ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__equals__takeWhile__sorted__rev) ).
thf(10569,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Orev @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( ( B @ ( C @ ( A @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Ofilter ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_OtakeWhile ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).
thf(1047,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_Onat @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__number__of) ).
thf(8660,plain,
! [A: $i,B: $i] :
( ( ( c_Int_Onat @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_Onat @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(2864,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__restrict__set) ).
thf(15974,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2864]) ).
thf(4515,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton_H) ).
thf(22477,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4515]) ).
thf(910,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I9_J) ).
thf(8209,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(4562,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2E) ).
thf(22656,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4562]) ).
thf(4231,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ? [D: $i,E: $i] :
( ( A @ ( C @ c_List_Olists ) @ ( E @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( B
= ( C @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists_Osimps) ).
thf(21408,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ? [D: $i,E: $i] :
( ( A @ ( C @ c_List_Olists ) @ ( E @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( B
= ( C @ c_List_Olist_ONil ) ) )
=> ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ? [D: $i,E: $i] :
( ( A @ ( C @ c_List_Olists ) @ ( E @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( B
= ( C @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4231]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__commutes) ).
thf(5009,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(4677,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Compl__self__eq) ).
thf(23093,plain,
! [A: $i,B: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4677]) ).
thf(3475,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__SUPR__fold__sup) ).
thf(18401,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( E @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3475]) ).
thf(2394,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__image__eq) ).
thf(14030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2394]) ).
thf(4705,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ ( E @ ( G @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ ( D @ ( c_fNot @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( G @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ ( C @ ( D @ c_Com_Ocom_OCond ) ) @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OIf) ).
thf(23217,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( D @ ( E @ ( G @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ ( D @ ( c_fNot @ ( tc_Com_Ostate @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( G @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
=> ( tc_HOL_Obool @ ( G @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ ( C @ ( D @ c_Com_Ocom_OCond ) ) @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( G @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4705]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I2_J) ).
thf(5129,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(4062,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_List_Oset @ hAPP ) @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__remove1) ).
thf(20676,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_List_Oset @ hAPP ) @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4062]) ).
thf(683,axiom,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).
thf(7355,plain,
tc_Code__Numeral_Ocode__numeral @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(4392,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton_H) ).
thf(22057,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4392]) ).
thf(3903,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__imp__surj) ).
thf(20138,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ ( D @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3903]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ hAPP ) @ ( D @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_Random_Opick ) @ hAPP ) )
= ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ hAPP ) @ ( D @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Random_Opick ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ hAPP ) @ ( D @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_Random_Opick ) @ hAPP ) )
= ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Osnd ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick_Osimps) ).
thf(8038,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ hAPP ) @ ( D @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_Random_Opick ) @ hAPP ) )
= ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ hAPP ) @ ( D @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Random_Opick ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ hAPP ) @ ( D @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_Random_Opick ) @ hAPP ) )
= ( B @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Osnd ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(4031,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(20567,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4031]) ).
thf(2792,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) )
= ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oremove) ).
thf(15679,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) )
= ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2792]) ).
thf(2041,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__int__def) ).
thf(12615,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2041]) ).
thf(1629,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__lemma) ).
thf(11035,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629]) ).
thf(787,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__code__numeral__def) ).
thf(7759,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1862,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).
thf(11960,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1862]) ).
thf(2919,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olexord ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_List_Olexord ) @ ( A @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Relation_Otrans ) )
=> ( B @ ( E @ c_List_Olexord ) @ ( A @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__trans) ).
thf(16192,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olexord ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_List_Olexord ) @ ( A @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Relation_Otrans ) )
=> ( B @ ( E @ c_List_Olexord ) @ ( A @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2919]) ).
thf(1917,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( A @ ( F @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [G: $i] : ( B @ ( C @ ( G @ ( E @ ( F @ c_Fun_Obij__betw ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cantor__Bernstein) ).
thf(12162,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( A @ ( F @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [G: $i] : ( B @ ( C @ ( G @ ( E @ ( F @ c_Fun_Obij__betw ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1917]) ).
thf(2930,axiom,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
thf(16235,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2930]) ).
thf(1535,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( A @ ( A @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__comp__eq) ).
thf(10681,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( A @ ( A @ ( C @ ( C @ c_Relation_Oconverse ) @ hAPP ) @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535]) ).
thf(4159,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ounion__disjoint) ).
thf(21125,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4159]) ).
thf(2981,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
thf(16458,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2981]) ).
thf(623,axiom,
tc_Nat_Onat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(7140,plain,
tc_Nat_Onat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(3428,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( E @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__map__eq__map) ).
thf(18220,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Oset @ hAPP ) @ ( B @ ( E @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3428]) ).
thf(895,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__special_I2_J) ).
thf(8162,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(3086,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Com_Ocom_OWhile ) )
= ( A @ ( B @ c_Com_Ocom_OWhile ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).
thf(16871,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_Com_Ocom_OWhile ) )
= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ) )
& ( ( ( C @ ( D @ c_Com_Ocom_OWhile ) )
= ( A @ ( B @ c_Com_Ocom_OWhile ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3086]) ).
thf(2076,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
thf(12739,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2076]) ).
thf(4357,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinfinite) ).
thf(21932,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4357]) ).
thf(2190,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Oreplicate ) ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Oreplicate ) ) @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__append__same) ).
thf(13207,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_List_Oreplicate ) ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Oreplicate ) ) @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2190]) ).
thf(3961,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).
thf(20333,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3961]) ).
thf(4590,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(22761,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4590]) ).
thf(1977,axiom,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__code) ).
thf(12380,plain,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL )
=> ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) )
& ( ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1977]) ).
thf(7147,plain,
( ! [A: $i] :
( ( c_Int_OPls = A )
=> ( c_Int_OPls
= ( A @ c_Int_OBit0 ) ) )
& ! [A: $i] :
( ( c_Int_OPls
= ( A @ c_Int_OBit0 ) )
=> ( c_Int_OPls = A ) ) ),
inference(miniscope,[status(thm)],[7146]) ).
thf(7148,plain,
! [B: $i,A: $i] :
( ( ( c_Int_OPls
= ( B @ c_Int_OBit0 ) )
| ( c_Int_OPls != B ) )
& ( ( c_Int_OPls = A )
| ( c_Int_OPls
!= ( A @ c_Int_OBit0 ) ) ) ),
inference(cnf,[status(esa)],[7147]) ).
thf(7150,plain,
! [A: $i] :
( ( c_Int_OPls
= ( A @ c_Int_OBit0 ) )
| ( c_Int_OPls != A ) ),
inference(cnfConj,[status(thm)],[7148]) ).
thf(7152,plain,
! [A: $i] :
( ( ( A @ c_Int_OBit0 )
= c_Int_OPls )
| ( c_Int_OPls != A ) ),
inference(lifteq,[status(thm)],[7150]) ).
thf(7153,plain,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
inference(simp,[status(thm)],[7152]) ).
thf(4187,axiom,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(21248,plain,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4187]) ).
thf(1790,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).
thf(11680,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1790]) ).
thf(634,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).
thf(7171,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(2923,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_List_Oreplicate ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__replicate) ).
thf(16207,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_List_Oreplicate ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2923]) ).
thf(1320,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(9767,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(824,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
thf(7883,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(2174,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Int) ).
thf(13133,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2174]) ).
thf(4650,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(22993,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C = B ) )
& ( ( C = B )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4650]) ).
thf(4091,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__leq @ ( D @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omax__weak @ ( C @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omax__weak @ ( C @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmax__insertI) ).
thf(20831,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__leq @ ( D @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omax__weak @ ( C @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omax__weak @ ( C @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4091]) ).
thf(1299,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 @ hAPP ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_ONil @ ( B @ ( B @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__def) ).
thf(9711,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 @ hAPP ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_ONil @ ( B @ ( B @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(2990,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3mod ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3mod ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z3mod__def) ).
thf(16507,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3mod ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3mod ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2990]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append) ).
thf(6131,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(2207,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastLessThan) ).
thf(13257,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2207]) ).
thf(1393,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( D @ c_List_Oset @ hAPP ) @ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ c_List_Oset @ hAPP ) )
= ( A @ ( D @ c_List_Oset @ hAPP ) ) )
=> ( B = A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__sorted__distinct__set__unique) ).
thf(10041,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( D @ c_List_Oset @ hAPP ) @ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( ( B @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ c_List_Oset @ hAPP ) )
= ( A @ ( D @ c_List_Oset @ hAPP ) ) )
=> ( B = A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(4163,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__geq) ).
thf(21144,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4163]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) )
= ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__filter) ).
thf(5954,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) )
= ( A @ ( B @ ( C @ c_List_Ofilter ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(656,axiom,
tc_Nat_Onat @ class_Lattices_Osemilattice__inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
thf(7259,plain,
tc_Nat_Onat @ class_Lattices_Osemilattice__inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(2366,axiom,
! [A: $i,B: $i] : ( A @ ( B @ tc_prod ) @ class_Nat_Osize ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Nat_Osize) ).
thf(13905,plain,
! [A: $i,B: $i] : ( A @ ( B @ tc_prod ) @ class_Nat_Osize ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2366]) ).
thf(1728,axiom,
! [A: $i] :
( ( ( A @ c_Int_OBit1 )
= c_Int_OMin )
<=> ( A = c_Int_OMin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).
thf(11437,plain,
! [A: $i] :
( ( ( A = c_Int_OMin )
=> ( ( A @ c_Int_OBit1 )
= c_Int_OMin ) )
& ( ( ( A @ c_Int_OBit1 )
= c_Int_OMin )
=> ( A = c_Int_OMin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728]) ).
thf(2322,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
thf(13753,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2322]) ).
thf(2221,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I53_J) ).
thf(13314,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2221]) ).
thf(3728,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ohom__commute) ).
thf(19432,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3728]) ).
thf(1174,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__1) ).
thf(9183,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(4184,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffI) ).
thf(21241,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4184]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
<=> ( C
= ( D @ c_List_Olist_ONil @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_List_Orev @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__eq__Cons__iff) ).
thf(5430,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C
= ( D @ c_List_Olist_ONil @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_List_Orev @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( C
= ( D @ c_List_Olist_ONil @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_List_Orev @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(2876,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).
thf(16006,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2876]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_List_Olist_ONil )
= ( A @ ( B @ c_List_Orev @ hAPP ) ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__rev__conv) ).
thf(5356,plain,
! [A: $i,B: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( ( B @ c_List_Olist_ONil )
= ( A @ ( B @ c_List_Orev @ hAPP ) ) ) )
& ( ( ( B @ c_List_Olist_ONil )
= ( A @ ( B @ c_List_Orev @ hAPP ) ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__list__update) ).
thf(7712,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1479,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(10418,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479]) ).
thf(3212,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Union) ).
thf(17355,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) )
= ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3212]) ).
thf(1258,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
thf(9523,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(594,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__code__numeral__code) ).
thf(7029,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( B @ ( c_Code__Numeral_Oof__nat @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Code__Numeral_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(4720,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(23269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4720]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(5764,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(2486,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff) ).
thf(14475,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2486]) ).
thf(2193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I18_J) ).
thf(13220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2193]) ).
thf(1867,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff__nat) ).
thf(11975,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1867]) ).
thf(2179,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
thf(13165,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2179]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( A @ ( B @ ( I @ ( E @ ( J @ ( F @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( C @ ( D @ ( G @ ( I @ ( H @ ( J @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( E @ ( F @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ ( I @ ( J @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( G @ ( I @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( D @ ( F @ ( H @ ( J @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( G @ ( E @ ( H @ ( F @ c_Product__Type_Omap__pair ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Ocomp) ).
thf(6456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( A @ ( B @ ( I @ ( E @ ( J @ ( F @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( C @ ( D @ ( G @ ( I @ ( H @ ( J @ c_Product__Type_Omap__pair ) ) ) ) ) @ ( E @ ( F @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ ( I @ ( J @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ ( E @ ( G @ ( I @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( D @ ( F @ ( H @ ( J @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( G @ ( E @ ( H @ ( F @ c_Product__Type_Omap__pair ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(2113,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus1__not__zero) ).
thf(12848,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2113]) ).
thf(2060,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition) ).
thf(12681,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2060]) ).
thf(4105,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oinsert__remove) ).
thf(20913,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4105]) ).
thf(1930,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__le__nat) ).
thf(12213,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1930]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Ocommute) ).
thf(5884,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__mod__div) ).
thf(5477,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_List_Olinorder__class_Osorted__list__of__set ) )
= ( A @ ( B @ c_List_Oremdups ) @ ( B @ c_COMBI @ ( B @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__sort__remdups) ).
thf(5371,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_List_Olinorder__class_Osorted__list__of__set ) )
= ( A @ ( B @ c_List_Oremdups ) @ ( B @ c_COMBI @ ( B @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(3380,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Set_OPow @ hAPP ) )
= ( B @ c_Set_OPow @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBS ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_HOL_OEx @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__Compl) ).
thf(17989,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Set_OPow @ hAPP ) )
= ( B @ c_Set_OPow @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_member @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBS ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_HOL_OEx @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3380]) ).
thf(2195,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( F @ ( C @ c_List_Olistrelp ) ) ) )
=> ( A @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ ( C @ c_List_Olistrelp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_OCons) ).
thf(13225,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( F @ ( C @ c_List_Olistrelp ) ) ) )
=> ( A @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ ( C @ c_List_Olistrelp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2195]) ).
thf(2427,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ hBOOL ) )
<=> ! [D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__set__conv__all__nth) ).
thf(14208,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) )
=> ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ hBOOL ) )
=> ! [D: $i] :
( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2427]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_HOL_OThe ) )
= ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( C @ c_Product__Type_Ofst ) @ ( A @ ( B @ ( C @ tc_prod ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ ( C @ tc_prod ) @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_HOL_OThe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_The__split) ).
thf(7248,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_HOL_OThe ) )
= ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( C @ c_Product__Type_Ofst ) @ ( A @ ( B @ ( C @ tc_prod ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ ( C @ tc_prod ) @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_HOL_OThe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(3581,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep_Oequations) ).
thf(18847,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3581]) ).
thf(1620,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__number__of) ).
thf(10998,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
thf(9156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(3265,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__eq__zle) ).
thf(17544,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3265]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus) ).
thf(4885,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(3548,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1__nat) ).
thf(18699,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3548]) ).
thf(1305,axiom,
! [A: $i] :
( ( A @ c_Fun_Oid @ ( A @ ( A @ c_List_Omap ) @ hAPP ) )
= ( A @ tc_List_Olist @ c_Fun_Oid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oid) ).
thf(9728,plain,
! [A: $i] :
( ( A @ c_Fun_Oid @ ( A @ ( A @ c_List_Omap ) @ hAPP ) )
= ( A @ tc_List_Olist @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(3268,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Int__distrib) ).
thf(17561,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3268]) ).
thf(2096,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(12798,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2096]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).
thf(5014,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(2555,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Relation_Osingle__valued ) ) )
=> ( B @ ( C @ ( D @ c_Relation_Osingle__valued ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__subset) ).
thf(14774,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Relation_Osingle__valued ) ) )
=> ( B @ ( C @ ( D @ c_Relation_Osingle__valued ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2555]) ).
thf(1823,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_List_Obutlast ) @ ( A @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__butlast) ).
thf(11807,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_List_Obutlast ) @ ( A @ c_List_Odistinct @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1823]) ).
thf(1794,axiom,
! [A: $i] :
( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
thf(11695,plain,
! [A: $i] :
( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1794]) ).
thf(3104,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__less) ).
thf(16943,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3104]) ).
thf(3974,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(20378,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3974]) ).
thf(2167,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Orderings_Otop__class_Otop @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__fold__inf) ).
thf(13096,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Orderings_Otop__class_Otop @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2167]) ).
thf(2441,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( D @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__seg__image__imp__finite) ).
thf(14278,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) ) )
=> ( D @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2441]) ).
thf(2491,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__in) ).
thf(14490,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olinorder__class_OMax ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2491]) ).
thf(3871,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
thf(20022,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3871]) ).
thf(3205,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
thf(17323,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3205]) ).
thf(1436,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
thf(10205,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olexord ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ? [E: $i] :
( ( A @ ( E @ ( B @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( C @ ( E @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( B @ ( E @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) ) )
& ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ( ( B @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= C )
& ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__take__index__conv) ).
thf(5926,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ? [E: $i] :
( ( A @ ( E @ ( B @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( C @ ( E @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( B @ ( E @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) ) )
& ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ( ( B @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= C )
& ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( D @ c_List_Olexord ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_List_Olexord ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ? [E: $i] :
( ( A @ ( E @ ( B @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( D @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( C @ ( E @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( B @ ( E @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) ) )
& ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( ( ( B @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) )
= C )
& ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(960,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Enum_Osublists ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__sublists) ).
thf(8368,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Enum_Osublists ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(2017,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) )
= ( B @ ( C @ c_Relation_ORange ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Union) ).
thf(12515,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_Relation_ORange ) @ hAPP ) )
= ( B @ ( C @ c_Relation_ORange ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2017]) ).
thf(4149,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(21085,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4149]) ).
thf(1949,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(12272,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1949]) ).
thf(2386,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lists__conv__set) ).
thf(13986,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2386]) ).
thf(3484,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oidem) ).
thf(18435,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( A @ ( B @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3484]) ).
thf(4094,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost__int) ).
thf(20838,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4094]) ).
thf(3949,axiom,
c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I24_J) ).
thf(20297,plain,
c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3949]) ).
thf(1857,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD1) ).
thf(11943,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1857]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( A @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendL) ).
thf(6411,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( A @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(4047,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__if) ).
thf(20631,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4047]) ).
thf(2122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( E @ c_Fun_Oinj__on ) ) ) )
<=> ( C @ ( D @ ( A @ ( F @ ( B @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on__iff) ).
thf(12904,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( C @ ( D @ ( A @ ( F @ ( B @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( E @ c_Fun_Oinj__on ) ) ) ) )
& ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( B @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( C @ ( D @ ( A @ ( F @ ( B @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ c_Fun_Oinj__on ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2122]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__1__iff) ).
thf(6535,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(4421,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).
thf(22147,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4421]) ).
thf(2530,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinsert) ).
thf(14659,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2530]) ).
thf(2974,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__one) ).
thf(16426,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Oone__class_Oone @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ ( D @ ( E @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2974]) ).
thf(2505,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(14546,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2505]) ).
thf(1088,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Otranspose ) )
= ( A @ tc_List_Olist @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I1_J) ).
thf(8833,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ c_List_Olist_ONil @ ( A @ c_List_Otranspose ) )
= ( A @ tc_List_Olist @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(642,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
<=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != D )
=> ( ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
!= ( D @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).
thf(7199,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != D )
=> ( ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
!= ( D @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ) ) )
=> ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != D )
=> ( ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) )
!= ( D @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(2574,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryI) ).
thf(14843,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2574]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( D
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( D @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma) ).
thf(7851,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL )
=> ( ( D
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( D @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Divides_Odivmod__int__rel ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(4282,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__right) ).
thf(21630,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4282]) ).
thf(3714,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ c_Fun_Oid @ ( D @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex__id) ).
thf(19368,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ c_Fun_Oid @ ( D @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3714]) ).
thf(2907,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omin @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).
thf(16145,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Orderings_Oord__class_Omin @ ( D @ ( D @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2907]) ).
thf(4305,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subset__eq) ).
thf(21712,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4305]) ).
thf(3369,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
thf(17937,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3369]) ).
thf(1803,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_List_Olistrel1 ) )
= ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Relation_Oconverse ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__converse) ).
thf(11727,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_List_Olistrel1 ) )
= ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Relation_Oconverse ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1803]) ).
thf(3537,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(18628,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3537]) ).
thf(2341,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).
thf(13819,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2341]) ).
thf(26609,plain,
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8089,13558]) ).
thf(26610,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[26609]) ).
thf(26635,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Nat__Numeral_Oneg @ hAPP ) )
!= c_fTrue ),
inference(simp,[status(thm)],[26610]) ).
thf(2754,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib2) ).
thf(15540,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2754]) ).
thf(3247,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( G @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( D @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ ( D @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= ( A @ ( E @ ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( G @ c_Fun_Othe__inv__into ) ) ) @ ( C @ ( B @ ( G @ ( D @ c_Fun_Othe__inv__into ) ) ) @ ( F @ ( D @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__comp) ).
thf(17488,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( G @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( D @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( F @ ( D @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= ( A @ ( E @ ( B @ ( C @ ( G @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( G @ c_Fun_Othe__inv__into ) ) ) @ ( C @ ( B @ ( G @ ( D @ c_Fun_Othe__inv__into ) ) ) @ ( F @ ( D @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3247]) ).
thf(2250,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Enum_Osublists ) @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( B @ c_List_Oset @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Set_OPow @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublists__powset) ).
thf(13432,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Enum_Osublists ) @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( B @ c_List_Oset @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ c_Set_OPow @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2250]) ).
thf(2372,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i,F: $i] :
( D
= ( F @ ( E @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( A @ ( C @ c_List_Olexord ) @ ( D @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).
thf(13926,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i,F: $i] :
( D
= ( F @ ( E @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( A @ ( C @ c_List_Olexord ) @ ( D @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2372]) ).
thf(2870,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__insert__idem) ).
thf(15989,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Otimes__class_Otimes @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2870]) ).
thf(4347,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(21881,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4347]) ).
thf(2169,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( ( A
= ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__imp__eq__int) ).
thf(13101,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( ( A
= ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2169]) ).
thf(1391,axiom,
( c_FunDef_Omin__strict
= ( c_FunDef_Opair__less @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Omin__ext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__strict__def) ).
thf(10036,plain,
( c_FunDef_Omin__strict
= ( c_FunDef_Opair__less @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Omin__ext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(1672,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) )
= ( A @ ( C @ c_List_Otl @ hAPP ) @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__drop) ).
thf(11214,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Otl @ hAPP ) )
= ( A @ ( C @ c_List_Otl @ hAPP ) @ ( B @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_Random_Oselect__weight ) )
= ( A @ ( C @ c_Random_Oselect__weight ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__cons__zero) ).
thf(5159,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_Random_Oselect__weight ) )
= ( A @ ( C @ c_Random_Oselect__weight ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(2891,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) )
= ( C @ c_List_Olist_ONil ) )
<=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).
thf(16078,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) )
= ( C @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) )
= ( C @ c_List_Olist_ONil ) )
=> ! [D: $i] :
( ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2891]) ).
thf(1003,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(8521,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I2_J) ).
thf(5092,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(909,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( B @ c_List_Otl @ hAPP ) @ ( B @ c_List_Olinorder__class_Osorted ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__tl) ).
thf(8207,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
=> ( A @ ( B @ c_List_Otl @ hAPP ) @ ( B @ c_List_Olinorder__class_Osorted ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(29612,plain,
( ( ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8089,15263]) ).
thf(29613,plain,
( ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
!= ( c_fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[29612]) ).
thf(29642,plain,
( ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) )
!= c_fTrue ),
inference(simp,[status(thm)],[29613]) ).
thf(3003,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__greatest) ).
thf(16558,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3003]) ).
thf(2291,axiom,
! [A: $i] :
( ~ ( A @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__eq__ge__0) ).
thf(13614,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2291]) ).
thf(1667,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId @ ( B @ ( B @ c_Relation_OImage ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id) ).
thf(11194,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId @ ( B @ ( B @ c_Relation_OImage ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667]) ).
thf(1424,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ ( C @ ( I @ ( D @ ( K @ ( E @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( D @ ( H @ ( I @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( G @ ( E @ ( J @ ( K @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( H @ ( D @ ( J @ ( E @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Ocompositionality) ).
thf(10168,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ ( C @ ( I @ ( D @ ( K @ ( E @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( D @ ( H @ ( I @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( G @ ( E @ ( J @ ( K @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( H @ ( D @ ( J @ ( E @ c_Product__Type_Omap__pair ) ) ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(4302,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( E @ ( D @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).
thf(21702,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( E @ ( D @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4302]) ).
thf(962,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).
thf(8373,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1891,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__fun__def) ).
thf(12076,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1891]) ).
thf(1196,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_OdropWhile ) ) )
= ( A @ ( B @ ( D @ ( C @ ( tc_HOL_Obool @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_OdropWhile ) ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__map) ).
thf(9271,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_OdropWhile ) ) )
= ( A @ ( B @ ( D @ ( C @ ( tc_HOL_Obool @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_List_OdropWhile ) ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(2723,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OThe ) @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__vimage__singleton) ).
thf(15416,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_HOL_OThe ) @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2723]) ).
thf(462,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( A @ c_COMBI @ ( A @ ( A @ c_List_Olinorder__class_Oinsort__key ) ) @ ( A @ tc_List_Olist @ ( A @ c_Finite__Set_Ofun__left__comm ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__insort) ).
thf(6488,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
=> ( A @ c_COMBI @ ( A @ ( A @ c_List_Olinorder__class_Oinsort__key ) ) @ ( A @ tc_List_Olist @ ( A @ c_Finite__Set_Ofun__left__comm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(2036,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert__distrib) ).
thf(12583,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2036]) ).
thf(3925,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Inf__fold__inf) ).
thf(20222,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3925]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult2__eq) ).
thf(6735,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(1013,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_List_Orotate ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__conv__mod) ).
thf(8557,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_List_Orotate ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(2398,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Fun_Oid @ ( A @ ( C @ ( B @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__id) ).
thf(14050,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Fun_Oid @ ( A @ ( C @ ( B @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2398]) ).
thf(3417,axiom,
! [A: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__nat__eq) ).
thf(18157,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3417]) ).
thf(1194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( D @ ( C @ c_List_Orotate ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__map) ).
thf(9265,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( D @ ( C @ c_List_Orotate ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(2319,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ! [I: $i] :
( ( G @ ( H @ c_List_Oset @ hAPP ) @ ( I @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( I @ ( D @ hAPP ) @ ( E @ ( F @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( I @ ( B @ hAPP ) @ ( C @ ( E @ ( F @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) )
=> ( ( G @ ( A @ ( C @ hAPP ) @ ( D @ ( F @ ( F @ ( H @ c_COMBC ) ) @ hAPP ) @ ( H @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( G @ ( A @ ( B @ ( E @ ( E @ ( H @ c_COMBC ) ) @ hAPP ) @ ( H @ ( E @ c_List_Ofoldl ) ) ) @ hAPP ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__apply) ).
thf(13738,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ! [I: $i] :
( ( G @ ( H @ c_List_Oset @ hAPP ) @ ( I @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( I @ ( D @ hAPP ) @ ( E @ ( F @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( I @ ( B @ hAPP ) @ ( C @ ( E @ ( F @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) )
=> ( ( G @ ( A @ ( C @ hAPP ) @ ( D @ ( F @ ( F @ ( H @ c_COMBC ) ) @ hAPP ) @ ( H @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( G @ ( A @ ( B @ ( E @ ( E @ ( H @ c_COMBC ) ) @ hAPP ) @ ( H @ ( E @ c_List_Ofoldl ) ) ) @ hAPP ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2319]) ).
thf(3900,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__upto) ).
thf(20127,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( B @ c_List_Oupto ) @ ( tc_Int_Oint @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3900]) ).
thf(976,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(8424,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__ident) ).
thf(6558,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(4315,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).
thf(21757,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4315]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).
thf(9002,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(1755,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
<=> ( ? [F: $i] :
( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
& ( D
= ( E @ c_List_Olist_ONil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).
thf(11548,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ? [F: $i] :
( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
& ( D
= ( E @ c_List_Olist_ONil ) ) ) )
=> ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ? [F: $i] :
( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
& ( D
= ( E @ c_List_Olist_ONil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755]) ).
thf(3776,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_Nat__Transfer_Onat__set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).
thf(19632,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Ois__nat )
=> ( A @ ( B @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_Nat__Transfer_Onat__set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3776]) ).
thf(1943,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OPow @ hAPP ) @ ( A @ ( D @ c_Set_OPow @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Pow__subset) ).
thf(12252,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ c_Set_OPow @ hAPP ) @ ( A @ ( D @ c_Set_OPow @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1943]) ).
thf(2327,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__below__fold1__iff) ).
thf(13770,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2327]) ).
thf(3586,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less__dividend) ).
thf(18865,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3586]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_List_Oupt ) @ ( C @ ( tc_Nat_Onat @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__upt) ).
thf(5741,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_List_Oupt ) @ ( C @ ( tc_Nat_Onat @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(2176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ~ ( A @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
& ( ( A @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__insert__iff) ).
thf(13139,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ~ ( A @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
& ( ( A @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( A @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
& ( ( A @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2176]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(8516,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(2949,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( D @ hAPP ) @ hBOOL )
=> ( E @ ( B @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) )
=> ( B @ ( D @ ( C @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( A @ tc_prod ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__same__fst) ).
thf(16321,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( D @ hAPP ) @ hBOOL )
=> ( E @ ( B @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) )
=> ( B @ ( D @ ( C @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( A @ tc_prod ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2949]) ).
thf(4375,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).
thf(21991,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4375]) ).
thf(2011,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( A @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).
thf(12503,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( A @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( D @ ( C @ c_Relation_ORange ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2011]) ).
thf(3858,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).
thf(19979,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3858]) ).
thf(3092,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(16901,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3092]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__simps_I2_J) ).
thf(5441,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( A @ ( C @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(4456,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( F @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I2) ).
thf(22267,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( F @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4456]) ).
thf(4578,axiom,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_Set_OPow @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cantors__paradox) ).
thf(22716,plain,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ c_Set_OPow @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4578]) ).
thf(3271,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0) ).
thf(17575,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3271]) ).
thf(3602,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osize_I2_J) ).
thf(18919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ tc_Hoare__Mirabelle_Otriple @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3602]) ).
thf(3289,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__replicate) ).
thf(17649,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3289]) ).
thf(3186,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).
thf(17252,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( B @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3186]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(7278,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__number__of__left) ).
thf(5339,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(3255,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ ( A @ ( B @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__leI) ).
thf(17516,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ ( A @ ( B @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3255]) ).
thf(3947,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).
thf(20292,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3947]) ).
thf(1314,axiom,
! [A: $i,B: $i] : ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ c_List_Oremdups ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remdups__leq) ).
thf(9752,plain,
! [A: $i,B: $i] : ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ c_List_Oremdups ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(3323,axiom,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).
thf(17765,plain,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Int_Oint @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3323]) ).
thf(2791,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq2) ).
thf(15673,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ ( D @ ( E @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( E @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2791]) ).
thf(2934,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(16256,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2934]) ).
thf(1699,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(11326,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699]) ).
thf(1182,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__append__conv) ).
thf(9215,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( C
= ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(4545,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
thf(22592,plain,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4545]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I31_J) ).
thf(5036,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(2072,axiom,
! [A: $i] : ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zle__0) ).
thf(12729,plain,
! [A: $i] : ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2072]) ).
thf(1446,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( C @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__overwrite) ).
thf(10237,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( C @ ( B @ ( C @ ( D @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Olist__update ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(4865,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1329,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ tc_prod ) @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip_Osimps_I1_J) ).
thf(9795,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ tc_prod ) @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(2806,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(15726,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2806]) ).
thf(4546,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un) ).
thf(22596,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4546]) ).
thf(1230,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OposDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg) ).
thf(9414,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_OposDivAlg ) @ ( c_Divides_OnegateSnd @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(2666,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
thf(15213,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2666]) ).
thf(1815,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Bit1) ).
thf(11776,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Nat__Numeral_Oneg @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1815]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( B @ c_Divides_Opdivmod ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBB ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_fequal @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBS ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Divides_Opdivmod ) @ ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) @ ( c_fequal @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__code) ).
thf(5642,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( A @ ( B @ c_Divides_Opdivmod ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBB ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_fequal @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ c_COMBS ) ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Divides_Opdivmod ) @ ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) @ ( c_fequal @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oapsnd ) ) ) @ hAPP ) ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Divides_Odivmod__int ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(2268,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(13517,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2268]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__minus) ).
thf(6393,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(4234,axiom,
! [A: $i] :
( ( A @ c_Int_Oint__ge__less__than )
= ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__ge__less__than__def) ).
thf(21436,plain,
! [A: $i] :
( ( A @ c_Int_Oint__ge__less__than )
= ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ ( c_fconj @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ tc_prod ) @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4234]) ).
thf(4430,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert2) ).
thf(22179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4430]) ).
thf(1645,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(11099,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645]) ).
thf(3617,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
thf(18980,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3617]) ).
thf(564,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__ident) ).
thf(6929,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1781,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_OdropWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).
thf(11649,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_OdropWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781]) ).
thf(1190,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(9250,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(571,axiom,
! [A: $i] :
( ( A @ c_Code__Numeral_OSuc__code__numeral @ ( tc_Code__Numeral_Ocode__numeral @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osize_I4_J) ).
thf(6952,plain,
! [A: $i] :
( ( A @ c_Code__Numeral_OSuc__code__numeral @ ( tc_Code__Numeral_Ocode__numeral @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(2000,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__commute) ).
thf(12466,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2000]) ).
thf(1055,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__code__numeral__def) ).
thf(8706,plain,
! [A: $i,B: $i] :
( ( ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( B @ ( c_Code__Numeral_Onat__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(3663,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Opartition ) ) )
= ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I1_J) ).
thf(19161,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Opartition ) ) )
= ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3663]) ).
thf(4153,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).
thf(21104,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) )
= ( A @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Big__Operators_Olattice_OInf__fin ) ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4153]) ).
thf(1150,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
thf(9083,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) )
& ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(1817,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__unique) ).
thf(11784,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1817]) ).
thf(1460,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(10355,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(2028,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ ( C @ c_COMBK ) @ ( D @ ( C @ ( A @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ tc_fun ) @ ( D @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).
thf(12555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ ( C @ c_COMBK ) @ ( D @ ( C @ ( A @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ tc_fun ) @ ( D @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2028]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I3_J) ).
thf(5110,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(4626,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).
thf(22892,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4626]) ).
thf(4044,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).
thf(20616,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4044]) ).
thf(1681,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__div__cancel) ).
thf(11246,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681]) ).
thf(4183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( D @ ( C @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( B @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( D @ ( C @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( B @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) )
& ( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( D @ ( C @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( B @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= A ) )
& ( ( D @ ( C @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( B @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__if) ).
thf(21228,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( D @ ( C @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( B @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( D @ ( C @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( B @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) )
& ( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( D @ ( C @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( B @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= A ) )
& ( ( D @ ( C @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( A @ ( B @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ c_If @ ( B @ ( F @ ( F @ tc_fun ) @ ( F @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_fun ) @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4183]) ).
thf(3653,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oremove) ).
thf(19119,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olinorder__class_OMax ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMax ) )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3653]) ).
thf(764,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oinsert ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset__insert) ).
thf(7684,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Oinsert ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(725,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).
thf(7525,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(1614,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_List_Olist_Olist__case ) ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).
thf(10981,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_List_Olist_Olist__case ) ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614]) ).
thf(1690,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B )
<=> ( A
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__self__conv) ).
thf(11290,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( C @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) )
& ( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( C @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690]) ).
thf(807,axiom,
! [A: $i] :
( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).
thf(7819,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(605,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Relation_OId @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__unfold) ).
thf(7076,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Relation_OId @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(3979,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( D @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ ( E @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__nat__ivl) ).
thf(20397,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( D @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ ( E @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3979]) ).
thf(3389,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I8_J) ).
thf(18042,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3389]) ).
thf(2675,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ tc_prod ) @ ( F @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Product__Type_Osnd ) @ ( F @ ( D @ ( D @ ( E @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( F @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_Ofst ) @ ( F @ ( E @ ( D @ ( E @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Times) ).
thf(15245,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ tc_prod ) @ ( F @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Product__Type_Osnd ) @ ( F @ ( D @ ( D @ ( E @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( F @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_Ofst ) @ ( F @ ( E @ ( D @ ( E @ tc_prod ) @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2675]) ).
thf(1263,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) )
= ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( C @ c_Product__Type_Ofst ) @ ( A @ ( B @ ( C @ tc_prod ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ ( C @ tc_prod ) @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Eps__split) ).
thf(9547,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) )
= ( B @ ( C @ c_Product__Type_Osnd ) @ ( B @ ( C @ c_Product__Type_Ofst ) @ ( A @ ( B @ ( C @ tc_prod ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ ( C @ tc_prod ) @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(1986,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I6_J) ).
thf(12412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1986]) ).
thf(4297,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Opair__less @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI2) ).
thf(21680,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Opair__less @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4297]) ).
thf(643,axiom,
( ( c_fTrue @ ( tc_HOL_Obool @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I3_J) ).
thf(7214,plain,
( ( c_fTrue @ ( tc_HOL_Obool @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(1597,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__ge__zero) ).
thf(10896,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__constant) ).
thf(4848,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( D @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(7538,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(3089,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb2) ).
thf(16891,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3089]) ).
thf(3208,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( E @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).
thf(17340,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( E @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3208]) ).
thf(2983,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(16462,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2983]) ).
thf(869,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ ( B @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__zipI2) ).
thf(8066,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ ( B @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_List_Odistinct @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(2145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) )
=> ( E = F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
thf(12996,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) )
=> ( E = F ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) )
=> ( E = F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2145]) ).
thf(3615,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist__ex1 ) ) )
<=> ? [D: $i] :
( ! [E: $i] :
( ( ( E @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E = D ) )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex1__iff__raw) ).
thf(18963,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ! [E: $i] :
( ( ( E @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E = D ) )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Olist__ex1 ) ) ) )
& ( ( A @ ( B @ ( C @ c_List_Olist__ex1 ) ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( ( E @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( E = D ) )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3615]) ).
thf(1333,axiom,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Nat__Transfer_Ois__nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J) ).
thf(9810,plain,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_Nat__Transfer_Ois__nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(2525,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
thf(14640,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2525]) ).
thf(3160,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
thf(17172,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3160]) ).
thf(3819,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
thf(19792,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3819]) ).
thf(3429,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(18227,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3429]) ).
thf(3115,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
thf(16971,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3115]) ).
thf(1480,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Equiv__Relations_Oequivp ) )
=> ( ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__symp) ).
thf(10421,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Equiv__Relations_Oequivp ) )
=> ( ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ tc_prod ) @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__zip) ).
thf(7880,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ tc_prod ) @ c_List_Otake @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Ozip ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
thf(7352,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(2740,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).
thf(15484,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2740]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_List_Oupto ) )
= ( tc_Int_Oint @ c_List_Olist_ONil ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_List_Oupto ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupto ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto__rec__number__of) ).
thf(6750,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_List_Oupto ) )
= ( tc_Int_Oint @ c_List_Olist_ONil ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ c_List_Oupto ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oupto ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(855,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( ( ~ ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( D @ ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( ( D @ ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) )
= B ) ) )
& ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( A @ ( B @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( D
= ( B @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv__if) ).
thf(7987,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ~ ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( D @ ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( ( D @ ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) )
= B ) ) )
& ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( A @ ( B @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( D
= ( B @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ) ) )
=> ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( ~ ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( D @ ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( ( D @ ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) )
= B ) ) )
& ( ( B @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( A @ ( B @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( D
= ( B @ ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(4567,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Obot )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
thf(22679,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Obot )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4567]) ).
thf(2375,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).
thf(13937,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2375]) ).
thf(3041,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Oconcat ) )
= ( B @ c_List_Olist_ONil ) )
<=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( B @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__eq__Nil__conv) ).
thf(16696,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( B @ c_List_Olist_ONil ) ) )
=> ( ( A @ ( B @ c_List_Oconcat ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ c_List_Oconcat ) )
= ( B @ c_List_Olist_ONil ) )
=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
= ( B @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3041]) ).
thf(2094,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(12793,plain,
! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2094]) ).
thf(1686,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).
thf(11258,plain,
c_Int_OPls != c_Int_OMin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Osemiring__0 )
& ( C @ class_Rings_Odvd ) )
=> ( ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
<=> ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
thf(6155,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Osemiring__0 )
& ( C @ class_Rings_Odvd ) )
=> ( ( ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
& ( ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(4017,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Ofilter ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__filter) ).
thf(20515,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Ofilter ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4017]) ).
thf(1978,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_fNot @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__not) ).
thf(12384,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( c_fNot @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_fNot @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1978]) ).
thf(737,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Ofoldr ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__transpose) ).
thf(7584,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Otranspose ) @ ( B @ tc_List_Olist @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Omax @ ( B @ tc_List_Olist @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( B @ tc_List_Olist @ c_List_Ofoldr ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(4700,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert) ).
thf(23197,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4700]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__add) ).
thf(6807,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__Suc) ).
thf(7227,plain,
! [A: $i,B: $i] :
( ( ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Nat__Numeral_Oneg @ ( c_fNot @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_fimplies @ ( tc_Int_Oint @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Int_Opred @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ c_HOL_OLet ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(3959,axiom,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(20329,plain,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3959]) ).
thf(2337,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__eq__zless) ).
thf(13807,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2337]) ).
thf(3236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int) ).
thf(17441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3236]) ).
thf(2116,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ c_Relation_ODomain ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__rtrancl) ).
thf(12872,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ c_Relation_ODomain ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2116]) ).
thf(718,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update_Osimps_I1_J) ).
thf(7506,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ c_List_Olist__update ) @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(2554,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
thf(14764,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2554]) ).
thf(1134,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__converse__trancl) ).
thf(9023,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(1042,axiom,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl) ).
thf(8643,plain,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(2286,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__insert) ).
thf(13601,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Relation_ORange ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Relation_ORange ) @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2286]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
=> ( A @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__appendI) ).
thf(5637,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
=> ( A @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(2430,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
=> ( ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__mono__one__left) ).
thf(14225,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Oone__class_Oone ) ) )
=> ( ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2430]) ).
thf(3752,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ hBOOL ) )
<=> ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( F @ ( B @ hAPP ) @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__UN) ).
thf(19528,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( F @ ( B @ hAPP ) @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ hBOOL ) ) )
=> ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ hBOOL ) )
=> ! [F: $i] :
( ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( F @ ( B @ hAPP ) @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3752]) ).
thf(2466,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Orderings_Olinorder )
& ( E @ class_Complete__Lattice_Ocomplete__lattice ) )
=> ( ( A @ ( B @ ( E @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SUP__iff) ).
thf(14390,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Orderings_Olinorder )
& ( E @ class_Complete__Lattice_Ocomplete__lattice ) )
=> ( ( ? [F: $i] :
( ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( A @ hAPP ) @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2466]) ).
thf(4161,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).
thf(21131,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ) ) )
& ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4161]) ).
thf(582,axiom,
! [A: $i] :
( ( A @ c_Relation_OId @ ( A @ ( A @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ c_Relation_OId ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Id) ).
thf(6993,plain,
! [A: $i] :
( ( A @ c_Relation_OId @ ( A @ ( A @ c_Relation_Oconverse ) @ hAPP ) )
= ( A @ c_Relation_OId ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(3197,axiom,
! [A: $i,B: $i] :
( ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Oantisym ) )
<=> ( A @ ( B @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__reflcl) ).
thf(17288,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Relation_Oantisym ) )
=> ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Oantisym ) ) )
& ( ( B @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Relation_Oantisym ) )
=> ( A @ ( B @ c_Relation_Oantisym ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3197]) ).
thf(4356,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono2) ).
thf(21930,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4356]) ).
thf(3459,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).
thf(18323,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3459]) ).
thf(3241,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( B @ hAPP ) @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( B @ hAPP ) @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Transitive__Closure_Otrancl ) @ ( C @ c_Wellfounded_Owf ) )
=> ? [D: $i] :
! [E: $i] :
( ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( D @ ( B @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__weak__decr__stable) ).
thf(17456,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( B @ hAPP ) @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( B @ hAPP ) @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Transitive__Closure_Otrancl ) @ ( C @ c_Wellfounded_Owf ) )
=> ? [D: $i] :
! [E: $i] :
( ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( D @ ( B @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3241]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i] : ( A @ ( D @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__power) ).
thf(6209,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] : ( A @ ( D @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(4653,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv2) ).
thf(23013,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_Set_OCollect @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4653]) ).
thf(2347,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Wellfounded_Owf ) )
<=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).
thf(13837,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) )
& ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2347]) ).
thf(2202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( c_fequal @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Hilbert__Choice_OEps ) )
= ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Eps__split__eq) ).
thf(13247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( c_fequal @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Hilbert__Choice_OEps ) )
= ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2202]) ).
thf(2445,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( D @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( D @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oreindex) ).
thf(14298,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__mult )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( D @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( D @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2445]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold__right) ).
thf(6373,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
thf(5061,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( F @ ( G @ ( H @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( B @ ( C @ ( F @ ( D @ ( E @ ( H @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
=> ( ( G @ ( A @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ c_Equiv__Relations_Ocongruent ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2__implies__congruent) ).
thf(6383,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( F @ ( G @ ( H @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( B @ ( C @ ( F @ ( D @ ( E @ ( H @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
=> ( ( G @ ( A @ ( H @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ c_Equiv__Relations_Ocongruent ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(4195,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) )
= ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_COMBI @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ ( B @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_Oinsert @ ( B @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__def) ).
thf(21277,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) )
= ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_COMBI @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ ( B @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_Oinsert @ ( B @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4195]) ).
thf(1065,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__numeral__code_I6_J) ).
thf(8758,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(1251,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmod__mult__2) ).
thf(9504,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(3270,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanAtMost) ).
thf(17572,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3270]) ).
thf(876,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).
thf(8093,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(4249,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__is__inj) ).
thf(21500,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Obij__betw ) ) ) ) )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4249]) ).
thf(398,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I4_J) ).
thf(6205,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(4632,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
<=> ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
thf(22918,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
=> ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4632]) ).
thf(2030,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__upt) ).
thf(12560,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2030]) ).
thf(1358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Wellfounded_Oacc ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
thf(9895,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Wellfounded_Oacc ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(4072,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I2_J) ).
thf(20735,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4072]) ).
thf(3761,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
thf(19573,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3761]) ).
thf(2958,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).
thf(16363,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Finite__Set_Ofun__left__comm ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2958]) ).
thf(2731,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(15444,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) )
=> ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2731]) ).
thf(3789,axiom,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin__Inf) ).
thf(19689,plain,
! [A: $i,B: $i] :
( ( B @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ c_Big__Operators_Olattice__class_OInf__fin ) )
= ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3789]) ).
thf(781,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).
thf(7740,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) )
=> ( ( C @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( F @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__nthD) ).
thf(5280,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) )
=> ( ( C @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( F @ c_List_Onth @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(3551,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).
thf(18716,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3551]) ).
thf(2845,axiom,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I5_J) ).
thf(15894,plain,
! [A: $i,B: $i] :
( ( B @ c_Nat__Transfer_Onat__set )
=> ( ( A @ c_Nat__Transfer_Onat__set )
=> ( ( ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2845]) ).
thf(809,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_List_Orotate ) )
= ( A @ ( C @ c_List_Orotate ) @ ( B @ ( C @ c_List_Orotate ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__add) ).
thf(7829,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_List_Orotate ) )
= ( A @ ( C @ c_List_Orotate ) @ ( B @ ( C @ c_List_Orotate ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(747,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Oconcat ) )
= ( A @ ( C @ c_List_Oconcat ) @ ( B @ ( C @ c_List_Oconcat ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__append) ).
thf(7616,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_List_Olist @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Oconcat ) )
= ( A @ ( C @ c_List_Oconcat ) @ ( B @ ( C @ c_List_Oconcat ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( A @ ( A @ ( B @ hAPP ) @ ( C @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__map__same) ).
thf(7035,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( A @ ( A @ ( B @ hAPP ) @ ( C @ ( c_fequal @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( E @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ c_List_Olinorder__class_Osorted ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__append) ).
thf(5681,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(4635,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
thf(22943,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4635]) ).
thf(4595,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple__size ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osize_I1_J) ).
thf(22783,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple__size ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4595]) ).
thf(4350,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__sup__top) ).
thf(21898,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4350]) ).
thf(1178,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(9193,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less) ).
thf(6082,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(693,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__div__2__gt__zero) ).
thf(7387,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(2439,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
thf(14269,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ocard @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2439]) ).
thf(1695,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__Cons) ).
thf(11309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Ofoldl ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter_Osimps_I2_J) ).
thf(8437,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(4685,axiom,
tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Nat__Transfer_Onat__set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).
thf(23120,plain,
tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Nat__Transfer_Onat__set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4685]) ).
thf(2801,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__idem) ).
thf(15711,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2801]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Min) ).
thf(5046,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
thf(6595,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(1144,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).
thf(9055,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(4388,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__empty) ).
thf(22044,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4388]) ).
thf(2800,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__refl__on) ).
thf(15709,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2800]) ).
thf(2518,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
thf(14610,plain,
! [A: $i] :
( ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2518]) ).
thf(1278,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) ).
thf(9633,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Int_Oint @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Olinordered__idom )
& ( C @ class_Int_Onumber__ring ) )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of) ).
thf(5236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Olinordered__idom )
& ( C @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1375,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Nitpick_Osetsum_H ) ) ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Nitpick_Osetsum_H ) ) ) )
= ( C @ c_List_Odistinct @ ( B @ ( C @ c_List_Oset @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Hilbert__Choice_OEps ) @ ( A @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).
thf(9969,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Nitpick_Osetsum_H ) ) ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Nitpick_Osetsum_H ) ) ) )
= ( C @ c_List_Odistinct @ ( B @ ( C @ c_List_Oset @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Hilbert__Choice_OEps ) @ ( A @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__take__nth__drop) ).
thf(7088,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ c_List_Otake @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(2612,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) )
& ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_OF__eq) ).
thf(14988,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( ~ ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) )
& ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ ( C @ ( D @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2612]) ).
thf(2905,axiom,
tc_Nat_Onat @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
thf(16142,plain,
tc_Nat_Onat @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2905]) ).
thf(1023,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__drop__take) ).
thf(8585,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(4245,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
thf(21490,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4245]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(5219,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(905,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
thf(8189,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oremove1 ) ) @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( B @ ( D @ c_List_Oremove1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__remove1) ).
thf(7263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oremove1 ) ) @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Ofilter ) @ hAPP ) @ ( B @ ( D @ c_List_Oremove1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(2563,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist__ex ) ) )
<=> ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__iff) ).
thf(14796,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Olist__ex ) ) ) )
& ( ( A @ ( B @ ( C @ c_List_Olist__ex ) ) )
=> ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( A @ ( C @ c_List_Oset @ hAPP ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2563]) ).
thf(2132,axiom,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV) ).
thf(12948,plain,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2132]) ).
thf(3373,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono__zero__right) ).
thf(17954,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3373]) ).
thf(4155,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).
thf(21113,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) @ ( A @ ( C @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Orderings_Oord__class_Omax @ ( C @ c_Big__Operators_Olattice_OSup__fin ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4155]) ).
thf(1854,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__eq__len) ).
thf(11935,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1854]) ).
thf(1210,axiom,
tc_Nat_Onat @ class_Lattices_Osemilattice__sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
thf(9335,plain,
tc_Nat_Onat @ class_Lattices_Osemilattice__sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(3354,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).
thf(17878,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3354]) ).
thf(4265,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oremove) ).
thf(21553,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ ( E @ ( E @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4265]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
thf(4955,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(4026,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
=> ~ ( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( ( A @ ( C @ c_Relation_Osym ) )
=> ~ ( A @ ( C @ c_Relation_Otrans ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivE) ).
thf(20548,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Equiv__Relations_Oequiv ) ) )
=> ~ ( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( ( A @ ( C @ c_Relation_Osym ) )
=> ~ ( A @ ( C @ c_Relation_Otrans ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4026]) ).
thf(4391,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
thf(22054,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4391]) ).
thf(768,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( D @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ ( E @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ ( E @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map1) ).
thf(7694,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Ozip ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( D @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( D @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ ( E @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ ( E @ ( D @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(3267,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(17557,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3267]) ).
thf(4413,axiom,
tc_HOL_Obool @ class_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
thf(22126,plain,
tc_HOL_Obool @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4413]) ).
thf(4660,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(23032,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) ) )
& ( ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4660]) ).
thf(1271,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
thf(9605,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(559,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
thf(6911,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(1245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ c_List_Obutlast ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ c_List_Obutlast ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Obutlast ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__butlast__appendI) ).
thf(9489,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ c_List_Obutlast ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ c_List_Obutlast ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Obutlast ) @ ( D @ c_List_Oset @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(4644,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Big__Operators_Olinorder__class_OMin ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Osingleton) ).
thf(22975,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Big__Operators_Olinorder__class_OMin ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4644]) ).
thf(1704,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Orev @ hAPP ) @ ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_OdropWhile ) ) )
= ( B @ ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Orev @ hAPP ) @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__neq__rev) ).
thf(11345,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_List_Orev @ hAPP ) @ ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_OdropWhile ) ) )
= ( B @ ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( C @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Orev @ hAPP ) @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704]) ).
thf(2829,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oclosed) ).
thf(15840,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [C: $i,D: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Big__Operators_Olattice__class_OSup__fin ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2829]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_OdropWhile ) ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
<=> ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_OtakeWhile ) ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).
thf(6548,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_OtakeWhile ) ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
=> ( ( C @ ( D @ ( E @ c_List_OdropWhile ) ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_OdropWhile ) ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_OtakeWhile ) ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(3556,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).
thf(18751,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Big__Operators_Olattice__class_OSup__fin ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3556]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( F @ c_Product__Type_Ofst ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_Osnd ) @ hAPP ) @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [H: $i,I: $i] :
( ( H @ ( I @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
=> ( I @ ( H @ ( B @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
=> ( D @ ( B @ ( A @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exE__realizer) ).
thf(8427,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( F @ c_Product__Type_Ofst ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_Osnd ) @ hAPP ) @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [H: $i,I: $i] :
( ( H @ ( I @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
=> ( I @ ( H @ ( B @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
=> ( D @ ( B @ ( A @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(4441,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UNIV) ).
thf(22215,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Ovimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4441]) ).
thf(4308,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
thf(21722,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4308]) ).
thf(2733,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
<=> ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= A )
& ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__def) ).
thf(15457,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= A )
& ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= A )
& ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2733]) ).
thf(1555,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(10758,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555]) ).
thf(2584,axiom,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__Abs__Integ) ).
thf(14873,plain,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( c_Int_Ointrel @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_OImage ) ) @ hAPP ) @ ( c_Int_OAbs__Integ @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2584]) ).
thf(4276,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I2_J) ).
thf(21598,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4276]) ).
thf(2771,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
thf(15597,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2771]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(7335,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(1770,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).
thf(11616,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770]) ).
thf(532,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__le) ).
thf(6797,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(4193,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge2) ).
thf(21272,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__sup )
=> ( B @ ( A @ ( C @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4193]) ).
thf(1894,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( D @ ( H @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( H @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( E @ hAPP ) @ ( B @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( E @ hAPP ) @ ( B @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ ( E @ hAPP ) @ ( B @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( B @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).
thf(12085,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( D @ ( H @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( H @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( E @ hAPP ) @ ( B @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ ( E @ hAPP ) @ ( B @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( C @ ( E @ hAPP ) @ ( B @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( B @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1894]) ).
thf(670,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
<=> ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).
thf(7299,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) )
=> ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
=> ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(2960,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).
thf(16368,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2960]) ).
thf(3307,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__le__0__conv) ).
thf(17701,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3307]) ).
thf(2987,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less__Suc2) ).
thf(16490,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ c_member @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Set_OCollect @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ocard @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2987]) ).
thf(4497,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I2_J) ).
thf(22405,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4497]) ).
thf(3696,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__apply) ).
thf(19298,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3696]) ).
thf(4355,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__eq__iff) ).
thf(21923,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4355]) ).
thf(695,axiom,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osize_I3_J) ).
thf(7392,plain,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(3048,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__code) ).
thf(16724,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( C @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3048]) ).
thf(1911,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( E @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greaterThanAtMost) ).
thf(12144,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( E @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1911]) ).
thf(2292,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
<=> ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).
thf(13620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) )
& ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2292]) ).
thf(1691,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib) ).
thf(11298,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691]) ).
thf(2620,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).
thf(15044,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2620]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ ( B @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( C @ c_Fun_Ocomp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__funpow) ).
thf(6119,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ ( B @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( C @ c_Fun_Ocomp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(3672,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Hilbert__Choice_OEps ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__def) ).
thf(19188,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Hilbert__Choice_OEps ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3672]) ).
thf(4433,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).
thf(22189,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4433]) ).
thf(2080,axiom,
c_Int_OInteg @ ( c_Int_OAbs__Integ @ ( c_Int_ORep__Integ @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ c_Typedef_Otype__definition ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition__Integ) ).
thf(12749,plain,
c_Int_OInteg @ ( c_Int_OAbs__Integ @ ( c_Int_ORep__Integ @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_Int_Oint @ c_Typedef_Otype__definition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2080]) ).
thf(3365,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I12_J) ).
thf(17922,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3365]) ).
thf(4725,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Oreplicate ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__replicate__Suc) ).
thf(23296,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Oreplicate ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4725]) ).
thf(2520,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Enum_On__lists ) ) @ ( C @ tc_List_Olist @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_List_Oset @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__n__lists) ).
thf(14621,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Enum_On__lists ) ) @ ( C @ tc_List_Olist @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) @ ( C @ c_List_Oset @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ ( c_fequal @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2520]) ).
thf(1470,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I6_J) ).
thf(10389,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(1176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( B @ c_List_OremoveAll ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll__filter__not) ).
thf(9188,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) @ ( C @ ( B @ c_List_OremoveAll ) @ hAPP ) )
= ( A @ ( D @ ( B @ c_List_Ofilter ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(4374,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__Int__atLeast) ).
thf(21988,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( B @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4374]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) )
= ( A @ ( C @ c_List_Orotate1 @ hAPP ) @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__rotate__swap) ).
thf(5172,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) )
= ( A @ ( C @ c_List_Orotate1 @ hAPP ) @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1338,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__idem) ).
thf(9838,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(4405,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__eq__Inter) ).
thf(22098,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4405]) ).
thf(903,axiom,
tc_HOL_Obool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(8184,plain,
tc_HOL_Obool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(2476,axiom,
tc_HOL_Obool @ class_Nat_Osize,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).
thf(14443,plain,
tc_HOL_Obool @ class_Nat_Osize,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2476]) ).
thf(1913,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Partial__Function_Ofun__lub ) ) ) ) ) )
= ( A @ ( F @ ( D @ tc_fun ) @ c_COMBI @ ( F @ ( D @ ( F @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( F @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ c_COMBB ) ) @ ( F @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( D @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( F @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ tc_fun ) @ c_HOL_OEx @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Set_OCollect @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__lub__def) ).
thf(12149,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Partial__Function_Ofun__lub ) ) ) ) ) )
= ( A @ ( F @ ( D @ tc_fun ) @ c_COMBI @ ( F @ ( D @ ( F @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fequal @ ( F @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ c_COMBB ) ) @ ( F @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( D @ tc_fun ) @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ ( F @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( F @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ c_COMBS ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( D @ tc_fun ) @ c_HOL_OEx @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( F @ ( D @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Set_OCollect @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1913]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).
thf(7553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Omonoid__add__class_Olistsum @ hAPP ) )
= ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ ( D @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(4779,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ class_Rings_Olinordered__idom ) ),
inference(cnfConj,[status(thm)],[4777]) ).
thf(2579,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product) ).
thf(14858,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Finite__Set_Ocard @ hAPP ) )
= ( A @ ( C @ c_Finite__Set_Ocard @ hAPP ) @ ( B @ ( D @ c_Finite__Set_Ocard @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2579]) ).
thf(1495,axiom,
! [A: $i,B: $i] :
( ( ~ ( ( B @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Random_Olog ) )
= ( B @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ c_Random_Olog ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Random_Olog ) )
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_log_Osimps) ).
thf(10482,plain,
! [A: $i,B: $i] :
( ( ~ ( ( B @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Random_Olog ) )
= ( B @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( B @ c_Random_Olog ) @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ c_Random_Olog ) )
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).
thf(4004,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__0__iff) ).
thf(20471,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4004]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( B @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ c_Int_Opred @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__number__of) ).
thf(5877,plain,
! [A: $i,B: $i] :
( ( B @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ c_Int_Opred @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(3691,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
thf(19279,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3691]) ).
thf(2123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Set_OCollect @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect) ).
thf(12908,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ c_Set_OCollect @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_Set_OCollect @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2123]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nat) ).
thf(6173,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Oabs__class_Oabs @ hAPP ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1496,axiom,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__code__numeral__code) ).
thf(10492,plain,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( tc_Code__Numeral_Ocode__numeral @ c_Int_Onumber__class_Onumber__of @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(3170,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
= ( c_fTrue @ ( A @ ( tc_HOL_Obool @ c_COMBK ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
thf(17205,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
= ( c_fTrue @ ( A @ ( tc_HOL_Obool @ c_COMBK ) @ hAPP ) @ ( A @ c_Set_OCollect @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3170]) ).
thf(2359,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
thf(13881,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2359]) ).
thf(3149,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Wellfounded_Omax__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Wellfounded_Omax__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Wellfounded_Omax__ext ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__compat) ).
thf(17108,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Wellfounded_Omax__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Wellfounded_Omax__ext ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Wellfounded_Omax__ext ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3149]) ).
thf(2749,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
thf(15521,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2749]) ).
thf(1877,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
thf(12017,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1877]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) )
=> ( B @ ( A @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( F @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__dropI) ).
thf(5312,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) )
=> ( B @ ( A @ ( E @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( F @ c_List_Odrop @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(3386,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [H: $i] :
( ( D @ ( H @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G != H )
=> ( ( ( G @ ( C @ hAPP ) )
= ( H @ ( C @ hAPP ) ) )
=> ( ( G @ ( C @ hAPP ) @ ( B @ hAPP ) )
= ( F @ c_Groups_Ozero__class_Ozero ) ) ) ) ) )
=> ( ( D @ ( C @ ( A @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( F @ ( A @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( E @ ( F @ ( A @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__nonzero) ).
thf(18014,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [H: $i] :
( ( D @ ( H @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G != H )
=> ( ( ( G @ ( C @ hAPP ) )
= ( H @ ( C @ hAPP ) ) )
=> ( ( G @ ( C @ hAPP ) @ ( B @ hAPP ) )
= ( F @ c_Groups_Ozero__class_Ozero ) ) ) ) ) )
=> ( ( D @ ( C @ ( A @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( F @ ( A @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( E @ ( F @ ( A @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3386]) ).
thf(4236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) )
<=> ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) )
& ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__Un) ).
thf(21443,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) )
& ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) ) )
=> ! [E: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [E: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) )
=> ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) )
& ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4236]) ).
thf(4205,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__bot )
=> ( ( B @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__right) ).
thf(21319,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Obounded__lattice__bot )
=> ( ( B @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4205]) ).
thf(860,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ! [D: $i] :
( ( B @ ( C @ ( A @ ( A @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( A @ ( A @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( D @ ( A @ ( A @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__eq__iff__zip__eq) ).
thf(8023,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( B @ ( C @ ( A @ ( A @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( A @ ( A @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( D @ ( A @ ( A @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) )
=> ( C = B ) )
& ( ( C = B )
=> ( ! [D: $i] :
( ( B @ ( C @ ( A @ ( A @ c_List_Ozip ) @ hAPP ) @ hAPP ) @ ( A @ ( A @ tc_prod ) @ c_List_Oset @ hAPP ) @ ( D @ ( A @ ( A @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) )
= ( B @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ c_Int_Osucc )
= ( A @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Bit0) ).
thf(4891,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 @ c_Int_Osucc )
= ( A @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(3593,axiom,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__zero__minus__one) ).
thf(18887,plain,
( ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Oone__class_Oone @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero @ ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Code__Numeral_Ocode__numeral @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3593]) ).
thf(2592,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__compose) ).
thf(14899,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ ( E @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2592]) ).
thf(2293,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ c_List_Oset @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( E @ c_List_Olist_Olist__size ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__estimation) ).
thf(13631,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ c_List_Oset @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( E @ c_List_Olist_Olist__size ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2293]) ).
thf(4695,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D != E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
thf(23156,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D != E ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D != E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4695]) ).
thf(3217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OSigma ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Union) ).
thf(17372,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( C @ ( D @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OSigma ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3217]) ).
thf(2213,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Osubset__idem) ).
thf(13289,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( A @ ( C @ c_Big__Operators_Olinorder__class_OMin ) @ ( C @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2213]) ).
thf(3349,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Oremove1 ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remove1__eq) ).
thf(17861,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_List_Oremove1 ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3349]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ ( C @ c_List_Olinorder__class_Osort__key ) ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sort) ).
thf(5458,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( D @ ( C @ c_List_Olinorder__class_Osort__key ) ) ) @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(2834,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI2) ).
thf(15855,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2834]) ).
thf(3426,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) )
= ( B @ ( C @ c_Relation_ODomain ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Union) ).
thf(18214,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( C @ c_Relation_ODomain ) @ hAPP ) )
= ( B @ ( C @ c_Relation_ODomain ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3426]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_List_Olist__all2 ) ) ) ) )
=> ( ( B @ ( C @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( G @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ ( G @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( H @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ ( H @ c_List_Olist__all2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__update__cong2) ).
thf(5618,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_List_Olist__all2 ) ) ) ) )
=> ( ( B @ ( C @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( G @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ ( G @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ ( H @ c_List_Olist__update ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ ( H @ c_List_Olist__all2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(4784,plain,
! [B: $i,A: $i] :
( ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Oring__1 ) ),
inference(cnf,[status(esa)],[4783]) ).
thf(4013,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oremove) ).
thf(20505,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4013]) ).
thf(1457,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_OwfP ) )
=> ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__acyclicP) ).
thf(10344,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_OwfP ) )
=> ( A @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_Set_OCollect @ hAPP ) @ ( B @ c_Wellfounded_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Random_Oselect__weight ) )
= ( A @ ( B @ c_Random_Opick ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ c_Product__Type_OPair ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ ( tc_Code__Numeral_Ocode__numeral @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ c_Random_Orange @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__def) ).
thf(4949,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Random_Oselect__weight ) )
= ( A @ ( B @ c_Random_Opick ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ c_Product__Type_OPair ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ c_Product__Type_Ofst ) @ ( tc_Code__Numeral_Ocode__numeral @ ( B @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( tc_Code__Numeral_Ocode__numeral @ c_List_Omonoid__add__class_Olistsum @ hAPP ) @ c_Random_Orange @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( B @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ ( tc_Code__Numeral_Ocode__numeral @ tc_prod ) @ c_Product__Type_Oscomp ) ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(4766,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_Rings_Oring__1 ) ),
inference(cnf,[status(esa)],[4765]) ).
thf(4767,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ class_Rings_Oring__1 )
| ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[4766]) ).
thf(1326,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ ( B @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ ( C @ tc_List_Olist @ ( D @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( C @ c_List_Omap ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Ocomp) ).
thf(9784,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ ( B @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ ( C @ tc_List_Olist @ ( D @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( C @ c_List_Omap ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(4510,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_OImage ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__eq__UN) ).
thf(22465,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Relation_OImage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Relation_OImage ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4510]) ).
thf(2197,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
thf(13230,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2197]) ).
thf(2472,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
thf(14426,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2472]) ).
thf(2212,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Oreplicate ) ) )
= ( A @ ( B @ ( E @ c_List_Oreplicate ) ) ) )
<=> ( ( ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( C = A ) )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__eq__replicate) ).
thf(13274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( C = A ) )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ c_List_Oreplicate ) ) )
= ( A @ ( B @ ( E @ c_List_Oreplicate ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Oreplicate ) ) )
= ( A @ ( B @ ( E @ c_List_Oreplicate ) ) ) )
=> ( ( ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( C = A ) )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2212]) ).
thf(2421,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) ) )
<=> ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff2) ).
thf(14155,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) )
= ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) ) )
=> ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2421]) ).
thf(1751,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( B @ ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ ( E @ ( D @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__the__inv__into) ).
thf(11534,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Obij__betw ) ) ) ) )
=> ( B @ ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ ( E @ ( D @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751]) ).
thf(3154,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [I: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( I @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( D @ hAPP ) )
= E ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).
thf(17123,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [I: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( I @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( D @ hAPP ) )
= E ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3154]) ).
thf(1775,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_OremoveAll ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_OremoveAll ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_OremoveAll ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll__append) ).
thf(11631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_OremoveAll ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_OremoveAll ) @ hAPP ) @ ( B @ ( C @ ( D @ c_List_OremoveAll ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1775]) ).
thf(2922,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__pos__nat) ).
thf(16203,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__mult__class_Osetprod ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2922]) ).
thf(2262,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( E @ c_List_OremoveAll ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_List_OremoveAll ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__removeAll__inj) ).
thf(13493,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( E @ c_List_OremoveAll ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_List_OremoveAll ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2262]) ).
thf(3065,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__def) ).
thf(16792,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3065]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(5261,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Ocompositionality) ).
thf(8179,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Omap ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( C @ c_List_Omap ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(2146,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olistsp ) @ ( B @ ( C @ c_List_Olistsp ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__inf__eq) ).
thf(13011,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olistsp ) @ ( B @ ( C @ c_List_Olistsp ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2146]) ).
thf(2657,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Orderings_Olinorder )
& ( E @ class_Complete__Lattice_Ocomplete__lattice ) )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( A @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__less__iff) ).
thf(15181,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ class_Orderings_Olinorder )
& ( E @ class_Complete__Lattice_Ocomplete__lattice ) )
=> ( ( ? [F: $i] :
( ( A @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( B @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2657]) ).
thf(4483,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeast @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc) ).
thf(22362,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeast @ hAPP ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeast @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4483]) ).
thf(3486,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__upt) ).
thf(18440,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oupt ) @ ( tc_Nat_Onat @ c_List_Oset @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3486]) ).
thf(4073,axiom,
tc_Nat_Onat @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
thf(20744,plain,
tc_Nat_Onat @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4073]) ).
thf(4470,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) )
= ( A @ c_Set_OBall ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__bool__eq) ).
thf(22313,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) )
= ( A @ c_Set_OBall ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4470]) ).
thf(547,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(6857,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(2266,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__fold__sup) ).
thf(13510,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Lattices_Osemilattice__sup__class_Osup @ ( C @ ( D @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2266]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(7602,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(2395,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I2_J) ).
thf(14033,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) )
& ( ( E
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2395]) ).
thf(3562,axiom,
! [A: $i,B: $i] :
( ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) ) )
<=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff2) ).
thf(18772,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) ) ) )
& ( ( ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ c_SetInterval_Oord_OatLeastAtMost ) ) ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3562]) ).
thf(4225,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Product__Type_OPair ) @ ( A @ ( C @ ( B @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( B @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__eta) ).
thf(21391,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Product__Type_OPair ) @ ( A @ ( C @ ( B @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( B @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4225]) ).
thf(1855,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Relation_Otrans ) )
=> ( ( D @ ( B @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transD) ).
thf(11938,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Relation_Otrans ) )
=> ( ( D @ ( B @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1855]) ).
thf(4548,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( C @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__comp__emptyR) ).
thf(22607,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ( A @ ( C @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ ( D @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4548]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__def) ).
thf(6254,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Product__Type_Osnd ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Product__Type_Ofst ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Divides_OnegDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos) ).
thf(5255,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Divides_OnegDivAlg ) @ ( tc_Int_Oint @ ( tc_Int_Oint @ c_Product__Type_Ofst ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(615,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int) ).
thf(7108,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(1827,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) ) )
=> ( B = A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__distinct__set__unique) ).
thf(11822,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( ( B @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
=> ( ( A @ ( C @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ c_List_Oset @ hAPP ) ) )
=> ( B = A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1827]) ).
thf(536,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__comp__rtrancl__eq) ).
thf(6810,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(3076,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( E @ c_COMBC ) ) @ hAPP ) @ ( D @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Set_OCollect @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__image__gen) ).
thf(16827,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( E @ c_COMBC ) ) @ hAPP ) @ ( D @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Set_OCollect @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3076]) ).
thf(3357,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(17893,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3357]) ).
thf(3226,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversepD) ).
thf(17404,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3226]) ).
thf(4605,axiom,
tc_HOL_Obool @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
thf(22826,plain,
tc_HOL_Obool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4605]) ).
thf(3032,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(16659,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3032]) ).
thf(3755,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I9_J) ).
thf(19545,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3755]) ).
thf(1312,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).
thf(9748,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(712,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).
thf(7478,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(523,axiom,
tc_Nat_Onat @ class_Orderings_Owellorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
thf(6761,plain,
tc_Nat_Onat @ class_Orderings_Owellorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).
thf(8966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(4506,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Un) ).
thf(22437,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4506]) ).
thf(2382,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__sign) ).
thf(13962,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2382]) ).
thf(2998,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__le__iff__disj) ).
thf(16543,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Olinorder )
=> ( ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2998]) ).
thf(4124,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_OremoveAll ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll__id) ).
thf(20984,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ c_List_Oset @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_List_OremoveAll ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4124]) ).
thf(4223,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(21372,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4223]) ).
thf(2933,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__eqI) ).
thf(16250,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Big__Operators_Olinorder__class_OMin ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2933]) ).
thf(1966,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oconcat ) @ ( B @ c_List_Oset @ hAPP ) )
= ( B @ c_List_Oset @ ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__concat) ).
thf(12348,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Oconcat ) @ ( B @ c_List_Oset @ hAPP ) )
= ( B @ c_List_Oset @ ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_List_Olist @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1966]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Odivmod__nat ) )
= ( A @ ( B @ c_Divides_Odivmod__nat__rel ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_HOL_OThe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__def) ).
thf(5664,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Odivmod__nat ) )
= ( A @ ( B @ c_Divides_Odivmod__nat__rel ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_HOL_OThe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) )
=> ( ( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( C @ c_List_OtakeWhile ) ) )
= ( B @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).
thf(6141,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) )
=> ( ( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ ( C @ c_List_OtakeWhile ) ) )
= ( B @ ( D @ ( C @ c_List_Otake @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(2588,axiom,
! [A: $i] :
~ ( tc_HOL_Obool @ ( A @ tc_List_Olist @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_List_Olist @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__listI) ).
thf(14884,plain,
! [A: $i] :
~ ( tc_HOL_Obool @ ( A @ tc_List_Olist @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_List_Olist @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2588]) ).
thf(3509,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).
thf(18523,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( C @ c_Orderings_Oord__class_Omin @ ( C @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3509]) ).
thf(3422,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMost) ).
thf(18181,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3422]) ).
thf(3536,axiom,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
thf(18620,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3536]) ).
thf(4646,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).
thf(22981,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4646]) ).
thf(3038,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Equiv__Relations_Ocongruent ) ) ) )
=> ( ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [H: $i] :
( ( F @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [I: $i] :
( ( F @ ( I @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( H @ ( C @ hAPP ) )
= ( I @ ( C @ hAPP ) ) )
=> ( E @ ( I @ ( H @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( B = A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__inject) ).
thf(16681,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( C @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Equiv__Relations_Ocongruent ) ) ) )
=> ( ( ( C @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( G @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) ) )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [H: $i] :
( ( F @ ( H @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [I: $i] :
( ( F @ ( I @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( H @ ( C @ hAPP ) )
= ( I @ ( C @ hAPP ) ) )
=> ( E @ ( I @ ( H @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( B = A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3038]) ).
thf(2684,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__injective) ).
thf(15273,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2684]) ).
thf(3918,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).
thf(20202,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3918]) ).
thf(4691,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__idemp) ).
thf(23133,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4691]) ).
thf(1822,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
<=> ( B
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__self__conv2) ).
thf(11799,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B
= ( C @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ) )
& ( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
=> ( B
= ( C @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1822]) ).
thf(2452,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( H @ ( I @ ( J @ ( K @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( A @ ( B @ ( E @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).
thf(14320,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( H @ ( I @ ( J @ ( K @ c_Finite__Set_Ofolding ) ) ) )
=> ( ( A @ ( B @ ( E @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2452]) ).
thf(2714,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__image__eq) ).
thf(15386,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2714]) ).
thf(419,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converse) ).
thf(6265,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_Oconverse ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1554,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
<=> ( A
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__is__Nil__conv) ).
thf(10750,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( C @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
=> ( A
= ( C @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).
thf(2220,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I8_J) ).
thf(13311,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) )
= ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2220]) ).
thf(3257,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(17520,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3257]) ).
thf(1083,axiom,
! [A: $i] :
( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
thf(8818,plain,
! [A: $i] :
( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(2400,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).
thf(14055,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__sup__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2400]) ).
thf(706,axiom,
tc_Int_Oint @ class_Rings_Ocomm__ring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(7424,plain,
tc_Int_Oint @ class_Rings_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(3895,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ ( B @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eqI) ).
thf(20114,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ ( B @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3895]) ).
thf(586,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).
thf(7003,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(1117,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oremdups ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remdups__id) ).
thf(8961,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Odistinct @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Oremdups ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(847,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
thf(7970,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(2433,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__subset) ).
thf(14236,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Complete__Lattice_Ocomplete__lattice )
=> ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2433]) ).
thf(1846,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A )
<=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
thf(11896,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= B )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) )
& ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1846]) ).
thf(918,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist__all ) ) )
<=> ! [D: $i] :
( ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__length) ).
thf(8232,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_List_Olist__all ) ) ) )
& ( ( A @ ( B @ ( C @ c_List_Olist__all ) ) )
=> ! [D: $i] :
( ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ c_List_Onth @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(4344,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).
thf(21868,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4344]) ).
thf(3692,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Relation_Ototal__on ) ) )
<=> ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__diff__Id) ).
thf(19281,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) )
=> ( C @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Relation_Ototal__on ) ) ) )
& ( ( C @ c_Relation_OId @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Relation_Ototal__on ) ) )
=> ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3692]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Osemiring__1 )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__Suc) ).
thf(4940,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Osemiring__1 )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(3285,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
!= ( B @ ( A @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_impossible__Cons) ).
thf(17634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
!= ( B @ ( A @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3285]) ).
thf(4791,plain,
! [B: $i,A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Olinordered__idom ) ),
inference(cnfConj,[status(thm)],[4790]) ).
thf(39451,plain,
! [B: $i,A: $i] :
( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ class_Rings_Olinordered__idom ) ),
inference(rewrite,[status(thm)],[4791,7678]) ).
thf(1883,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( D @ ( B @ ( A @ ( F @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( C @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( F @ ( C @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( C @ ( E @ tc_prod ) @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Sigma) ).
thf(12047,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ocomm__monoid__add )
=> ( ( D @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( D @ ( G @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
=> ( ( D @ ( B @ ( A @ ( F @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ ( E @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( F @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ ( E @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( C @ ( E @ c_Product__Type_OSigma ) @ hAPP ) @ hAPP ) @ ( A @ ( F @ ( C @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( F @ ( C @ ( E @ tc_prod ) @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1883]) ).
thf(3407,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
<=> ( ? [C: $i,D: $i] :
( ( C @ ( B @ c_List_Olinorder__class_Osorted ) )
& ! [E: $i] :
( ( C @ ( B @ c_List_Oset @ hAPP ) @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( D @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( A
= ( C @ ( D @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_Osimps) ).
thf(18098,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Olinorder )
=> ( ( ( ? [C: $i,D: $i] :
( ( C @ ( B @ c_List_Olinorder__class_Osorted ) )
& ! [E: $i] :
( ( C @ ( B @ c_List_Oset @ hAPP ) @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( D @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( A
= ( C @ ( D @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) )
=> ( A @ ( B @ c_List_Olinorder__class_Osorted ) ) )
& ( ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
=> ( ? [C: $i,D: $i] :
( ( C @ ( B @ c_List_Olinorder__class_Osorted ) )
& ! [E: $i] :
( ( C @ ( B @ c_List_Oset @ hAPP ) @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( D @ ( B @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( A
= ( C @ ( D @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3407]) ).
thf(4408,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Oneg__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Oneg__single ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__single__def) ).
thf(22107,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Oneg__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Oneg__single ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4408]) ).
thf(3863,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ class_Enum_Oenum )
& ( D @ class_Orderings_Oorder ) )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__fun_I2_J) ).
thf(19999,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ class_Enum_Oenum )
& ( D @ class_Orderings_Oorder ) )
=> ( ( ( ( A @ ( B @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( c_fequal @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3863]) ).
thf(3820,axiom,
! [A: $i,B: $i,C: $i] :
~ ( tc_Nat_Onat @ ( C @ tc_fun ) @ c_List_Olist_ONil @ ( C @ c_List_Omeasures ) @ ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measures_I1_J) ).
thf(19794,plain,
! [A: $i,B: $i,C: $i] :
~ ( tc_Nat_Onat @ ( C @ tc_fun ) @ c_List_Olist_ONil @ ( C @ c_List_Omeasures ) @ ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3820]) ).
thf(2156,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel ) @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel_ONil) ).
thf(13061,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel ) @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2156]) ).
thf(3215,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
thf(17365,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( A @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3215]) ).
thf(710,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) )
<=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).
thf(7442,plain,
! [A: $i,B: $i] :
( ( ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) )
=> ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(64156,plain,
$false,
inference(e,[status(thm)],[19887,13373,19204,9929,8062,21624,5509,10007,21729,6085,16054,15170,20503,11472,10609,13321,6387,19672,17803,18575,31129,18008,13162,7272,17537,20432,4835,21040,13859,6669,12607,11445,16928,17358,5857,15564,19772,17072,7854,4909,17986,15418,7691,11372,5329,20014,17684,26625,10452,12116,19481,33616,12526,19101,21908,21439,6712,16501,4729,19062,11504,21595,9180,16604,10520,18610,13783,8114,9754,21871,23255,20300,22792,9833,19594,13058,19623,8338,10730,7100,20559,45790,7798,20973,10134,12753,18761,9731,20544,13933,9685,12731,15573,5654,23194,10743,22133,6512,15055,10944,17175,17998,8266,22820,6172,19148,6448,19117,11998,5778,23914,10319,9676,16533,9864,7072,13405,8646,10363,9411,11763,18723,5733,11318,6263,8475,15413,20124,21326,10987,11385,4728,18154,8755,10901,11527,22047,12507,12812,14944,13768,16092,15380,22257,8200,20990,17774,16950,16248,12549,22485,6868,17656,12500,11175,5444,13869,17326,18691,35877,9342,19127,23056,6057,7040,12575,9020,7888,6063,12674,22242,15066,19713,12030,15698,8883,14895,22158,13834,21645,8129,7935,5141,10198,12334,12649,7358,6918,20798,8434,7164,10234,7409,20520,23065,5820,22397,21720,13712,7008,20922,21149,14880,20748,23021,18388,5696,23219,6695,15267,7641,6744,5292,10542,16765,18193,16619,10673,16830,15314,13255,9383,15770,22698,9456,18233,16308,15795,18459,11409,10567,6813,20400,9324,20658,18549,21849,18365,8811,9704,20954,20320,22279,5297,15816,13159,8463,19438,14937,19081,13548,13525,14662,15293,12415,17929,9998,5625,19391,9717,20484,12774,7368,20405,13424,8447,8271,6830,9469,16730,5224,7332,9191,14377,20601,22910,18635,17046,12896,13227,17815,7781,9572,17715,8563,22681,10125,10805,5529,21570,13811,18284,11724,5383,21812,14324,8988,5348,9759,21834,15579,13020,22508,18942,6732,9268,20081,13202,6194,17407,21748,18678,20305,9950,5501,4739,18824,22185,8320,17411,20537,16196,18184,18178,22030,6971,18356,6278,21889,12193,13187,17820,16481,22402,8182,18878,19044,6764,21047,11945,6505,14602,14382,5565,8551,22599,18805,22579,16413,20117,7697,17362,11029,5906,16947,12714,6675,19722,12568,4839,22448,10869,15263,22434,13747,14905,7556,9052,10881,11417,5288,8915,18897,11303,12097,8353,10346,15217,8490,14805,15948,13270,17946,11020,18438,20611,10715,18001,5316,16894,15130,16817,8298,29604,10511,22225,6515,22987,12158,10209,16804,13655,15885,5713,13692,10747,20468,9356,16150,11513,10827,22582,16376,15331,8385,39016,18240,6996,17202,18729,20066,22517,9961,21285,5178,17375,15611,13557,16965,6894,19098,19863,21343,19323,7980,14301,33695,6877,19191,17285,17258,22365,15514,18499,16555,13488,16630,17976,20011,22101,7400,7043,12617,7605,9625,14292,11228,37467,15683,17243,15072,22631,16668,18661,22547,22742,22379,21467,6236,13975,13469,13238,10336,7018,21716,6570,14521,18531,5227,20280,6466,15482,7944,16868,9064,5252,5977,20386,15637,15863,8086,12833,18563,6268,5486,20662,9292,18090,9746,15590,19915,21948,16849,20569,22051,11542,15202,20168,7079,18977,10474,16623,15723,23236,14645,23130,6381,22197,11930,11613,13997,22704,13251,17798,19012,7734,7136,18304,9027,13083,19839,9159,18992,9994,10071,21253,19518,7326,5056,5770,8472,18420,17843,13378,12257,12543,5903,18496,16268,20941,9708,23060,14716,12388,15295,14969,8165,17607,7343,8678,39017,5874,8546,18072,13447,11912,4760,17697,20376,17727,23112,12785,13223,21935,18171,12324,14871,9394,5750,20588,11151,22086,12062,15119,21274,19836,9946,20078,11250,20441,4775,17197,17428,20209,15104,5024,5797,5342,8603,8583,21592,17925,12879,13841,12394,12843,12254,21479,12351,17911,20707,18754,17036,15135,7241,7790,10955,6766,17415,18269,14737,21916,21017,14474,11068,12475,14793,20465,13679,5306,20541,17610,6242,15125,11844,12943,21188,8494,6039,19626,9067,10587,7825,13558,22974,8996,7418,20340,15229,8089,14690,8225,15286,14260,13821,9432,16287,22121,9464,10053,9988,11652,12956,14351,9332,12718,21825,14722,22710,6723,4761,7528,11010,15759,23123,14173,11087,7349,17017,10863,22777,5064,19895,5274,6066,11966,16325,21861,10221,21985,7771,22536,15426,21354,22182,7541,6506,14141,13636,8785,39012,11448,7877,18005,21064,4778,22745,22859,11178,12065,15663,5150,18782,17613,7867,16712,9909,16789,11812,5182,19851,8146,10174,6662,47783,22640,6434,12819,22254,15787,5289,21960,15092,19525,15441,11628,19710,12003,7743,15264,23140,5836,15087,8880,20508,22955,20418,7665,22304,19226,5461,21339,19327,14830,18236,16919,11040,11827,20049,8257,8770,17530,14164,20232,22585,7835,5744,22095,23057,16672,20408,16003,11986,16721,16740,14487,21394,22827,21367,17694,15819,18143,8054,22938,16716,8278,14002,22144,15633,18451,18565,16655,23383,19959,12920,10534,16757,6681,18617,22161,17677,10687,14633,12291,22551,15028,19658,23258,14758,20276,10850,11773,6905,5199,6396,18582,20364,16772,11609,18292,6502,17049,19827,5802,11510,5193,14103,18069,19223,9843,10074,22089,8468,6599,16584,22488,20027,8600,12269,5622,5480,22627,6365,12229,11115,11600,10967,18424,11741,9199,18982,8615,39006,9362,7728,8543,5829,16223,5942,39023,20647,4952,8220,15110,22498,14597,18856,12988,16394,15866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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW390+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/5.42 % Computer : n017.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Sat Sep 26 15:43:40 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/5.76 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 4.10/6.66 % [INFO] Parsing done (889ms).
% 4.10/6.68 % [INFO] Running in sequential loop mode.
% 4.85/7.04 % [INFO] eprover registered as external prover.
% 4.85/7.05 % [INFO] Scanning for conjecture ...
% 7.32/7.75 % [INFO] Found a conjecture (or negated_conjecture) and 5227 axioms. Running axiom selection ...
% 11.06/9.67 % [INFO] Axiom selection finished. Selected 4723 axioms (removed 504 axioms).
% 16.77/11.31 % [INFO] Problem is first-order (TPTP FOF).
% 17.17/11.41 % [INFO] Type checking passed.
% 17.17/11.42 % [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 ...
% 200.62/71.30 % External prover 'e' found a proof!
% 200.62/71.30 % [INFO] Killing All external provers ...
% 200.62/71.31 % Time passed: 65774ms (effective reasoning time: 64621ms)
% 200.62/71.31 % 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)>
% 200.62/71.35 % Axioms used in derivation (4723): fact_div__code__numeral__def, fact_minus__mult__left, fact_zmod__minus1__right, fact_wf__not__refl, fact_add__le__less__mono, fact_setsum__shift__lb__Suc0__0, fact_zadd__int, fact_rotate__def, fact_neg__le__0__iff__le, fact_order__le__neq__trans, fact_INT__simps_I6_J, fact_SUP1__I, fact_remdups_Osimps_I1_J, fact_rtrancl__Int__subset, fact_bex__empty, fact_Int__insert__left__if1, fact_card__partition, fact_Nat_Oadd__0__right, fact_self__quotient, fact_converseI, fact_insert__partition, fact_greaterThanLessThan__upto, fact_wmax__insertI, fact_converse__meet, fact_atLeastLessThan__upt, fact_all__nat, fact_insert__compr, fact_Un__absorb1, fact_Sigma__Diff__distrib2, fact_fold__graph__insert__swap, fact_int__mult, fact_xt1_I1_J, fact_image__uminus__atLeastAtMost, fact_less__eq__int__code_I14_J, fact_Inf__Sup, fact_less__eq__code__numeral__def, fact_le__SucI, fact_notin__set__remove1, fact_drop__Cons__number__of, fact_finite__greaterThanLessThan__int, fact_UN__simps_I3_J, arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1, fact_set__drop__subset, fact_min__max_OInf__fin_Oremove, fact_setsum__cases, fact_converse__rtrancl__induct2, fact_singleton__iff, fact_replicate__append__same, fact_divmod__nat__zero, fact_ivl__disj__un_I12_J, fact_wmin__emptyI, fact_neg__number__of__Bit0, fact_single__valued__Id__on, fact_nat__gcd_Opinduct, fact_divmod__nat__rel__divmod__nat, fact_numeral__2__eq__2, fact_append__Nil2, fact_insertCI, fact_list__all2__map2, fact_int__0, fact_Diff__insert__absorb, fact_concat_Osimps_I1_J, fact_wfP__SUP, fact_inf__eq__top__iff, fact_not__sum__power2__lt__zero, fact_card__image__le, arity_fun__Orderings_Oorder, fact_divmod__nat__base, fact_nth__Cons__0, fact_folding__image__simple__idem_Osubset__idem, fact_rel__pow__Suc__I, fact_nat_Osimps_I3_J, fact_wf__union__merge, fact_of__int__minus, fact_surj__f__inv__f, fact_le__imp__diff__is__add, fact_bij__betw__same__card, fact_Union__upper, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_one__code__numeral__code, fact_divmod__nat__rel__mult1__eq, fact_Numeral1__eq1__nat, fact_power__abs, fact_Compl__UNIV__eq, fact_wf, fact_set__zip, fact_vimage__insert, fact_nat__rec__number__of, fact_greaterThanAtMost__empty__iff, fact_gauss__sum, fact_ImageE, fact_min__max_Oinf__absorb2, fact_inj__graph, fact_zero__power2, fact_dvd_Oless__trans, fact_InterE, fact_Compl__UN, fact_length__filter__less, fact_folding__one_Osingleton, fact_lessThan__Suc__atMost, arity_Code____Numeral__Ocode____numeral__Rings_Odvd, fact_New__DSequence_Opos__map__def, fact_number__of__diff, fact_finite__vimageI, fact_wf__not__sym, fact_greaterThanLessThan__empty, fact_finite__UN__I, fact_power__strict__decreasing, fact_adjust__def, fact_min__max_OSup__fin_Oinsert, fact_return__list__def, fact_mult, fact_sorted__take, fact_rel__pow__E2, arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice, fact_lexn_Osimps_I1_J, fact_Sup__fin_Oinsert__remove, fact_pos__add__strict, fact_refl__onD2, fact_Int__lower1, fact_inv__def, fact_sorted__insort__insert, fact_wf__inv__image, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact_setsum__shift__lb__Suc0__0__upt, fact_drop__butlast, fact_sequence__trans, fact_sorted__append, fact_converse__converse, fact_minus__Bit0, fact_card__atLeastAtMost, fact_dropWhile_Osimps_I2_J, fact_rotate__is__Nil__conv, fact_pos__union__def, fact_setsum__constant, fact_finite_Oequations_I1_J, fact_sym__conv__converse__eq, fact_fold1Set_Ointros, fact_incr__mult__lemma, fact_Min__in, fact_in__set__conv__decomp, fact_le__inf__iff, fact_sup1I1, fact_Sigma__Un__distrib1, fact_transpose__column, fact_atLeastLessThan__empty__iff2, fact_mult__1__left, fact_diff__0__eq__0, fact_Ints__minus, fact_atLeastAtMost__singleton_H, fact_rel__simps_I6_J, fact_finite__lists__length__le, fact_zle__refl, fact_fold__sup__le__sup, fact_rel__pow__E, fact_inj__comp, fact_set__insort__insert, fact_transfer__nat__int__numerals_I1_J, fact_Field__empty, fact_Sigma__def, fact_nat__of__number, fact_bij__imp__bij__inv, fact_diff__add__inverse, fact_trans__less__add1, fact_comp__inj__on__iff, fact_less__eq__nat_Osimps_I2_J, fact_list__size__pointwise, fact_accp_Oequations, fact_setsum__divide__distrib, fact_nat__power__eq, fact_listrel__refl__on, fact_geometric__sum, fact_one__is__num__one, fact_inf__INFI__fold__inf, fact_setsum__Un__nat, fact_diff__nat__eq__if, fact_q__pos__lemma, fact_of__nat__add, fact_length__0__conv, fact_inj__imp__surj__inv, fact_card__Diff__subset__Int, fact_Inf__fin__Inf, fact_map__fst__zip, fact_subset__UNIV, fact_map__pair__inj__on, fact_inf2I, fact_ivl__disj__int_I5_J, fact_finite__greaterThanAtMost, fact_Range__Id, fact_notin__set__sublistI, fact_diff__0__right, fact_lexord__append__leftI, fact_setprod_Oinfinite, fact_setprod_Ounion__inter__neutral, fact_finite_OemptyI, fact_list__eq__iff__nth__eq, fact_div__pos__pos__1__number__of, fact_set__Cons__sing__Nil, fact_lexord__take__index__conv, fact_order__le__less__trans, fact_Compl__Times__UNIV1, fact_nat__add__left__commute, fact_set__append, fact_nat0__intermed__int__val, fact_transfer__morphism__nat__int, fact_nth__upt, fact_image__constant__conv, fact_zdiv__eq__0__iff, fact_Range__Int__subset, fact_inf__sup__aci_I4_J, fact_Image__Int__eq, fact_inf_Oassoc, fact_pair__lessI2, fact_neg__equal__0__iff__equal, fact_listrel1E, fact_inv__into__into, fact_INFI__bool__eq, fact_smax__insertI, fact_min__max_Osup__Inf1__distrib, fact_SetInterval_Otransfer__nat__int__set__function__closures, fact_Nitpick_Onumber__of__frac__def, fact_inj__on__diff__nat, fact_number__of__minus, fact_times__code__numeral__def, fact_inf__period_I4_J, fact_length__rotate, fact_lexord__lex, fact_Domain__Id, fact_insert__iff, fact_INT__Un, fact_zip__append1, fact_semiring__norm_I112_J, fact_atLeast__upt, fact_mod__mult2__eq, fact_image__insert, fact_negDivAlg_Opsimps, fact_setsum__empty, fact_ex__bij__betw__finite__nat, fact_INT__extend__simps_I2_J, fact_diff__bin__simps_I10_J, fact_dvdI, fact_part__equivp__transp, fact_of__int__power, fact_last__appendR, fact_foldr__max__sorted, fact_fun__left__comm__idem__insert, fact_take__drop, fact_greaterThan__subset__iff, fact_minus__fold__remove, fact_fst__eq__Domain, fact_sorted__map__same, fact_ivl__disj__int_I1_J, fact_min__diff, fact_zmod__number__of__Bit1, fact_bin__less__0__simps_I4_J, fact_card__gt__0__iff, fact_funpow_Osimps_I1_J, arity_Nat__Onat__Lattices_Olattice, fact_power__inject__base, fact_le__eq__less__or__eq, fact_triple_Osize_I1_J, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_fst__map__pair, fact_nat__less__cases, fact_Code__Numeral_Oof__nat__code, fact_of__int__int__eq, fact_nat__number__of__diff__1, fact_zero__less__int__conv, arity_prod__Finite__Set_Ofinite, fact_inf__Sup__absorb, fact_setsum__negf, fact_drop__upt, fact_bin__less__0__simps_I2_J, fact_one__is__add, fact_mult__nat__number__of, arity_prod__Enum_Oenum, fact_Compl__greaterThan, fact_diff__le__mono2, fact_minus__mult__right, fact_rev__swap, fact_Min_Ounion__inter, fact_xt1_I4_J, fact_listrel__Cons1, fact_zip__Nil, arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1, fact_ivl__disj__int_I13_J, fact_UnI1, fact_termination__basic__simps_I5_J, fact_insert__subset, fact_power__number__of__even__number__of, fact_Rep__Integ__inverse, fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J, fact_odd__nonzero, fact_list__all2__Cons, fact_diff__Suc, fact_SUP1__iff, fact_inj__int, fact_map_Osimps_I1_J, fact_code__numeral_Osimps_I3_J, fact_image__Pow__mono, fact_curry__split, fact_Ints__diff, fact_zip__takeWhile__snd, fact_less__int__code_I14_J, fact_zdiff__zmod__right, fact_injD, fact_nat__rec__Suc, fact_equivI, fact_set__take__subset__set__take, fact_transfer__int__nat__quantifiers_I2_J, fact_conversep_Oequations, fact_add__nat__number__of, fact_zminus__zminus, fact_pick_Osimps, fact_Ball__set__replicate, fact_folding__image__simple__idem_Oin__idem, fact_com_Osimps_I17_J, fact_divmod__nat__eq, fact_nat__number__of__add__1, fact_Inf__insert, fact_zpower__int, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_Suc__nat__eq__nat__zadd1, fact_mod__code__numeral__def, fact_zless__nat__conj, fact_below__fold1__iff, fact_rtranclD, fact_set__empty2, fact_setprod__zero__iff, fact_lists__IntI, fact_number__of__eq, fact_listsum__distinct__conv__setsum__set, fact_less__imp__le__nat, fact_less__supI1, fact_bot__apply, arity_Nat__Onat__Orderings_Oorder, fact_curry__def, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_UNION__empty__conv_I1_J, fact_drop__eq__Nil, fact_transfer__nat__int__numerals_I4_J, fact_fun__left__comm__idem__remove, fact_card__Diff__subset, fact_setsum__Un__zero, fact_le__Suc__number__of, fact_pred__nat__trancl__eq__le, fact_rel__comp__distrib, fact_setsum_Oreindex, fact_Inter__insert, fact_le__imp__0__less, fact_upto__empty, fact_com_Osize_I12_J, fact_sup__apply, fact_dvd__triv__right, fact_add__leD1, arity_sum__Finite__Set_Ofinite, fact_Times__Diff__distrib1, fact_UN__eq, fact_INF1__iff, fact_Compl__Int, fact_Max_Oin__idem, fact_converse__UNION, fact_Un__mono, fact_zpower__zmod, fact_finite__INT, fact_rel__simps_I49_J, fact_length__tl, fact_rel__simps_I27_J, fact_diff__number__of__eq, fact_finite__Collect__subsets, fact_greaterThan__iff, fact_Suc__diff__number__of, fact_of__nat__number__of__lemma, fact_zmult__int, fact_double__complement, fact_n__lists_Osimps_I2_J, fact_insort__key__remove1, fact_min__max_Obelow__fold1__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_n__less__m__mult__n, fact_fold__image__Un__one, fact_Transitive__Closure_Otrancl__into__trancl, fact_sup__Inf1__distrib, fact_fun__left__comm_Ofold__equality, fact_sup__compl__top, fact_unity__coeff__ex, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_Suc__times__mod__eq, fact_prod_Orecs, fact_transfer__int__nat__set__relations_I3_J, fact_of__int__add, arity_Int__Oint__Rings_Osemiring__1, fact_union__comp__emptyR, fact_UN__finite__subset, fact_mod__eq, fact_divide__numeral__1, fact_numeral__1__eq__Suc__0, fact_eq__Abs__Integ, fact_length__rotate1, fact_Inf__fin_Osingleton, fact_Suc__mono, fact_bij__betw__empty2, fact_zero__less__power, fact_image__uminus__atLeast, fact_concat__eq__Nil__conv, fact_Int__UNIV__right, fact_replicate__Suc, fact_atLeast__eq__iff, fact_distinct__remdups, fact_self__append__conv, fact_O__assoc, arity_Nat__Onat__Groups_Oordered__comm__monoid__add, fact_foldr__append, fact_less__nat__zero__code, fact_wmin__insertI, fact_hd__rev, fact_trancl__id, fact_List_Omap_Ocompositionality, fact_mono__Field, fact_fun__lub__def, fact_nat_Osize_I4_J, fact_divmod__int__rel__mod, fact_linorder__not__le, fact_finite__lists__length__eq, fact_min__ext__wf, fact_setsum__diff__nat, fact_equivp__transp, fact_setsum__setsum__restrict, fact_list__update__append, fact_finite, fact_add__less__mono, fact_curry__conv, fact_UN__simps_I10_J, fact_min__max_Oinf_Oleft__commute, fact_zadd__commute, arity_HOL__Obool__Lattices_Oboolean__algebra, fact_zless__int, fact_image__Int, fact_Sup__fin_Oeq__fold_H, fact_setprod__gen__delta, fact_setsum__atMost__Suc, fact_INT__simps_I10_J, fact_com_Osimps_I37_J, fact_IdI, fact_List_Omap_Ocomp, fact_lexn__length, arity_Nat__Onat__Groups_Omonoid__mult, fact_power__increasing, fact_diff__Suc__less, fact_insertI1, fact_transfer__int__nat__numerals_I2_J, fact_rel__comp__distrib2, fact_min__max_Oinf__sup__absorb, fact_mult__0, fact_vimage__UNIV, fact_Nitpick_Oone__frac__def, fact_in__listrel1__converse, fact_zip__Cons__Cons, fact_wf__no__loop, fact_int__eq__iff, fact_le__max__iff__disj, fact_Zero__int__def, fact_order__less__asym_H, fact_nat__number__of__add__left, fact_Un__empty__left, fact_sup2I2, fact_Inf__fin_Ounion__disjoint, fact_divmod__int__relI, fact_pair__box_Oinject, fact_folding__one_Ounion__inter, fact_flat__lub__def, fact_Max_OF__eq, fact_compl__sup__top, fact_list__all2I, fact_last__rev, fact_com_Osimps_I10_J, fact_UNIV__not__empty, fact_zip__map1, fact_not__zle__0__negative, fact_order__eq__refl, fact_Range__rtrancl, fact_image__constant, fact_ivl__disj__un_I15_J, fact_Un__insert__left, fact_triple_Osize_I2_J, fact_div__mod__equality_H, arity_Int__Oint__Lattices_Osemilattice__inf, fact_Int__Union, fact_Un__Pow__subset, fact_nat__number__of__Pls, fact_comm__monoid__big_Oinfinite, fact_List_Omember__def, fact_pred__nat__def, fact_div__nonpos__pos__le0, fact_dropWhile__eq__drop, fact_INFI__fold__inf, fact_INT__D, fact_of__int, fact_eq__neg__iff__add__eq__0, fact_scomp__scomp, fact_finite__induct, fact_folding__image__simple_Oeq__fold__g, fact_zero__code__numeral__code, fact_hoare__derivs_Oinsert, fact_transpose_Opsimps_I1_J, fact_less, fact_zero__le__zpower__abs, arity_fun__Lattices_Olattice, fact_max__ext__additive, arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult, fact_rtrancl_Ortrancl__refl, fact_ivl__disj__int_I4_J, fact_inf__absorb1, fact_com_Osimps_I46_J, fact_tl__take, fact_ex__bij__betw__nat__finite, fact_inj__image__mem__iff, fact_map__butlast, fact_equiv__def, fact_prod__eqI, fact_linorder__antisym__conv2, fact_image__add__atLeastLessThan, fact_min__max_Oless__infI1, fact_SUP2__E, fact_zero__less__diff, fact_conversep__noteq, fact_INT__eq, fact_remove1_Osimps_I1_J, fact_card_Oempty, fact_min__max_Oinf__Sup1__distrib, fact_acc_Osimps, fact_zmult2__lemma__aux4, arity_Nat__Onat__Lattices_Osemilattice__inf, fact_sorted__insort, fact_atLeastLessThanSuc, fact_min__max_Osup__inf__absorb, fact_hd__map, fact_setsum__insert, fact_finite__range__imageI, fact_diff__diff__cancel, fact_list__update__code_I2_J, fact_equiv__class__eq, fact_Int__atLeastAtMostR1, fact_Divides_Otransfer__int__nat__functions_I2_J, fact_measures__lesseq, fact_funpow__add, arity_HOL__Obool__Orderings_Opreorder, fact_rel__simps_I25_J, fact_nat__add__right__cancel, fact_distinct__append, fact_nat__1__add__number__of, fact_com_Osize_I5_J, fact_type__definition__Integ, fact_neg__le__iff__le, fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J, fact_com_Osimps_I2_J, fact_set__subset__Cons, fact_aset_I3_J, fact_quotient__diff1, fact_sorted__map__remove1, fact_gr0__conv__Suc, fact_Suc__eq__number__of, fact_linorder__neqE, fact_inf__Inf__fold__inf, fact_int__number__of__def, fact_o__eq__elim, fact_finite__Collect__bounded__ex, fact_div__le__dividend, fact_fold1__eq__fold, fact_inj__on__the__inv__into, fact_neg__0__less__iff__less, fact_listrelp_Oequations_I2_J, fact_last__drop, fact_listrel__subset__rtrancl__listrel1, fact_sup__assoc, fact_minus__code__numeral__def, fact_Compl__Un, fact_minus__shift__def, fact_distinct__rotate, fact_curryE, fact_eq__number__of__Suc, fact_Ex__inj__on__UNION__Sigma, fact_mod__pos__pos__trivial, fact_setsum__commute, fact_leI, fact_takeWhile__eq__all__conv, fact_the__inv__f__f, fact_min__max_Ole__iff__sup, fact_field__power__not__zero, fact_take__upt, fact_dvd_OatLeastLessThan__empty__iff2, fact_sup__inf__absorb, fact_Int__left__commute, fact_Min__insert, fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J, fact_one__div__nat__number__of, fact_listsum__const__mult, fact_empty__not__insert, fact_UN__extend__simps_I5_J, fact_image__vimage__eq, fact_SigmaE2, fact_trans__Id__on, fact_range, fact_tl__replicate, fact_less__special_I4_J, fact_nat__list__def, fact_rotate__map, fact_mult__le__mono2, help_c__fconj__3, fact_ivl__disj__un_I22_J, fact_zmod__zdiv__equality, fact_Suc__diff__diff, fact_image__Int__subset, fact_CollectI, fact_Suc__mod__eq__add3__mod, fact_nat__abs__mult__distrib, fact_divmod__int__def, fact_rtrancl__empty, fact_sym__trans__comp__subset, fact_nat__set__def, fact_Union__Int__subset, fact_Suc__le__mono, fact_distinct__zipI2, arity_Int__Oint__Orderings_Oord, fact_Cons__acc__listrel1I, fact_r__into__trancl_H, fact_mod__less, fact_power2__eq__imp__eq, fact_max__ext__compat, fact_Bex__set__list__ex, fact_rel__simps_I31_J, fact_rel__compI, fact_length__insort, fact_Min_Ounion__disjoint, fact_atLeast__iff, fact_Int__UN__distrib, fact_singleton__rev__conv, fact_power__number__of__odd, fact_setsum__lessThan__Suc, fact_surj__iff__all, fact_Un__UNIV__left, fact_filter__empty__conv, fact_setsum__right__distrib, fact_setsum__multicount, fact_inf__sup__ord_I2_J, fact_neg__imp__number__of__eq__0, fact_atLeastPlusOneLessThan__greaterThanLessThan__int, fact_infinite__UNIV__int, help_c__fequal__2, fact_UNION__empty__conv_I2_J, fact_mult__eq__self__implies__10, fact_Image__eq__UN, fact_wf__Int1, fact_acyclic__impl__antisym__rtrancl, fact_Pow__Compl, fact_le__neq__implies__less, fact_tranclD2, fact_wf__less, fact_Image__UN, fact_inf__sup__distrib2, fact_Min_Oeq__fold_H, fact_minus__add__cancel, fact_divmod__nat__rel__unique, fact_add__pos__nonneg, fact_expand__Suc, fact_power2__eq__square, fact_length__takeWhile__less__P__nth, fact_ivl__diff, fact_sublist__shift__lemma, fact_transfer__nat__int__numerals_I2_J, fact_atMost__eq__iff, fact_list__all__iff, fact_finite__code, fact_setprod__Un, fact_of__int__1, fact_anamorph_Osimps, fact_Collect__imp__eq, fact_snd__eqD, fact_filter__concat, fact_mult__numeral__1__right, fact_fun__Compl__def, fact_zle__linear, fact_append__eq__conv__conj, fact_neg__single__def, fact_INT__greaterThan__UNIV, fact_zero__le__one, fact_inj__on__id, fact_zmult__div__cancel, fact_folding_Oinsert, fact_comp__inj__on, fact_min__max_OSup__fin_Oin__idem, fact_List_Oset__insert, fact_Max__fin__set__fold, fact_min__max_Ole__iff__inf, fact_code__numeral_Osize_I4_J, fact_of__int__m1, fact_finite__Plus__UNIV__iff, fact_nat__add__distrib, fact_transfer__nat__int__set__relations_I3_J, fact_image__UN, fact_setprod__eq__1__iff, fact_ComplD, fact_measures__def, fact_setsum__reindex, 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% 200.62/71.35 % No. of inferences in proof: 9787
% 200.62/71.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 65774 ms resp. 64621 ms w/o parsing
% 220.45/75.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 221.11/75.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------