TSTP Solution File: SWW358+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW358+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:23:37 EDT 2023
% Result : Theorem 97.67s 29.58s
% Output : Refutation 100.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1420
% Syntax : Number of formulae : 2709 ( 810 unt; 133 typ; 0 def)
% Number of atoms : 6604 (2220 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 77909 ( 496 ~; 80 |; 588 &;73385 @)
% ( 234 <=>;3126 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 292 ( 292 >; 0 *; 0 +; 0 <<)
% Number of symbols : 135 ( 133 usr; 18 con; 0-6 aty)
% Number of variables : 10072 ( 0 ^;9920 !; 152 ?;10072 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_G_type,type,
v_G: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_mgt__call_type,type,
v_mgt__call: $i ).
thf(v_U_type,type,
v_U: $i ).
thf(class_Groups_Ocomm__monoid__mult_type,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(c_member_type,type,
c_member: $i > $i ).
thf(c_Lattices_Osemilattice__inf__class_Oinf_type,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_Finite__Set_Ofold__image_type,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(c_Lattices_Osemilattice__sup__class_Osup_type,type,
c_Lattices_Osemilattice__sup__class_Osup: $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Complete__Lattice_OSup__class_OSup_type,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Nitpick_Ofold__graph_H_type,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThan_type,type,
c_SetInterval_Oord__class_OgreaterThan: $i > $i ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i ).
thf(c_Set_OCollect_type,type,
c_Set_OCollect: $i > $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i ).
thf(c_Relation_OField_type,type,
c_Relation_OField: $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple_type,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Product__Type_OSigma_type,type,
c_Product__Type_OSigma: $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i ).
thf(c_Finite__Set_Ofun__left__comm__idem_type,type,
c_Finite__Set_Ofun__left__comm__idem: $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold_type,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofun__left__comm_type,type,
c_Finite__Set_Ofun__left__comm: $i > $i > $i > $o ).
thf(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: $i > $i ).
thf(c_Wellfounded_Owf_type,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(c_Wellfounded_Oacc_type,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_Wellfounded_Omax__ext_type,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(c_Fun_Ocomp_type,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(c_Complete__Lattice_OInf__class_OInf_type,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(c_Equiv__Relations_Oquotient_type,type,
c_Equiv__Relations_Oquotient: $i > $i ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofold__graph_type,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i ).
thf(c_Wellfounded_Omeasure_type,type,
c_Wellfounded_Omeasure: $i > $i ).
thf(c_Finite__Set_Ofolding__image_type,type,
c_Finite__Set_Ofolding__image: $i > $i > $i > $i > $i > $o ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(c_SetInterval_Oord__class_OatLeast_type,type,
c_SetInterval_Oord__class_OatLeast: $i > $i ).
thf(c_FunDef_Oreduction__pair_type,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Omin__strict_type,type,
c_FunDef_Omin__strict: $i ).
thf(c_FunDef_Omin__weak_type,type,
c_FunDef_Omin__weak: $i ).
thf(c_Big__Operators_Ocomm__monoid__add__class_Osetsum_type,type,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum: $i > $i > $i ).
thf(c_Fun_Obij__betw_type,type,
c_Fun_Obij__betw: $i > $i > $i > $i > $i > $o ).
thf(c_Wellfounded_Ofinite__psubset_type,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
thf(c_Set_OPow_type,type,
c_Set_OPow: $i > $i ).
thf(c_Product__Type_Oprod_Oprod__case_type,type,
c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(c_FunDef_Opair__less_type,type,
c_FunDef_Opair__less: $i ).
thf(c_FunDef_Omax__strict_type,type,
c_FunDef_Omax__strict: $i ).
thf(c_Wellfounded_Omax__extp_type,type,
c_Wellfounded_Omax__extp: $i > $i > $i > $i > $o ).
thf(c_Wellfounded_OwfP_type,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_Big__Operators_Ocomm__monoid__big_type,type,
c_Big__Operators_Ocomm__monoid__big: $i > $i > $i > $i > $i > $o ).
thf(c_Wellfounded_Omlex__prod_type,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_FunDef_Omax__weak_type,type,
c_FunDef_Omax__weak: $i ).
thf(c_Hilbert__Choice_Oinv__into_type,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_Fun_Oid_type,type,
c_Fun_Oid: $i > $i ).
thf(c_Finite__Set_Ofolding_type,type,
c_Finite__Set_Ofolding: $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofolding__idem_type,type,
c_Finite__Set_Ofolding__idem: $i > $i > $i > $i > $o ).
thf(c_Fun_Othe__inv__into_type,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__one_type,type,
c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).
thf(c_Finite__Set_Ofolding__one__idem_type,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_Predicate_OPowp_type,type,
c_Predicate_OPowp: $i > $i > $i ).
thf(c_COMBI_type,type,
c_COMBI: $i > $i ).
thf(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(c_Product__Type_Ocurry_type,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i ).
thf(c_Int_ORep__Integ_type,type,
c_Int_ORep__Integ: $i ).
thf(c_Int_OInteg_type,type,
c_Int_OInteg: $i ).
thf(c_If_type,type,
c_If: $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple__idem_type,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(v_wt_type,type,
v_wt: $i > $o ).
thf(v_c_type,type,
v_c: $i ).
thf(c_SetInterval_Oord_OatLeast_type,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastLessThan_type,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_type,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThanLessThan_type,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_type,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(v_P_type,type,
v_P: $i > $i > $o ).
thf(v_mgt_type,type,
v_mgt: $i > $i ).
thf(c_Option_Othe_type,type,
c_Option_Othe: $i > $i > $i ).
thf(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
thf(c_Com_Obody_type,type,
c_Com_Obody: $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_type,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThanAtMost_type,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(c_Typedef_Otype__definition_type,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_Quotient_OBabs_type,type,
c_Quotient_OBabs: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThan_type,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__empty_type,type,
c_New__Random__Sequence_Opos__empty: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__empty_type,type,
c_New__DSequence_Opos__empty: $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__rec_type,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Oneg__single_type,type,
c_New__Random__Sequence_Oneg__single: $i > $i ).
thf(c_New__DSequence_Oneg__single_type,type,
c_New__DSequence_Oneg__single: $i > $i > $i ).
thf(c_New__DSequence_Opos__map_type,type,
c_New__DSequence_Opos__map: $i > $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Omap_type,type,
c_Lazy__Sequence_Omap: $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Ohb__single_type,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(c_FunDef_Orp__inv__image_type,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__case_type,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__single_type,type,
c_New__Random__Sequence_Opos__single: $i > $i ).
thf(c_New__DSequence_Opos__single_type,type,
c_New__DSequence_Opos__single: $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__not__random__dseq_type,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__not__seq_type,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(c_Product__Type_Oprod_Oprod__rec_type,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Osingle_type,type,
c_Lazy__Sequence_Osingle: $i > $i ).
thf(c_New__Random__Sequence_Opos__union_type,type,
c_New__Random__Sequence_Opos__union: $i > $i > $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__union_type,type,
c_New__DSequence_Opos__union: $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Oempty_type,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(c_Lazy__Sequence_Oappend_type,type,
c_Lazy__Sequence_Oappend: $i > $i > $i > $i ).
thf(1130,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ F ) @ A ) )
& ( D
= ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
thf(5561,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ F ) @ A ) )
& ( D
= ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ F ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ F ) @ A ) )
& ( D
= ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ C ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__def) ).
thf(2612,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ C ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(408,axiom,
( ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__0) ).
thf(2778,plain,
( ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
thf(1995,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__code) ).
thf(3798,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ C @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ B @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__insert) ).
thf(3666,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).
thf(2427,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1036,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(5205,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ? [E: $i] :
( ( c_Fun_Oinj__on @ C @ B @ E @ D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ B @ E ) @ D ) ) @ A ) ) )
<=> ? [E: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ C @ E ) @ A )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).
thf(3172,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( ? [E: $i] :
( ( c_Fun_Oinj__on @ C @ B @ E @ D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ B @ E ) @ D ) ) @ A ) ) )
=> ? [E: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ C @ E ) @ A )
= D ) )
& ( ? [E: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ C @ E ) @ A )
= D )
=> ? [E: $i] :
( ( c_Fun_Oinj__on @ C @ B @ E @ D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ B @ E ) @ D ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(1076,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).
thf(5385,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(1206,axiom,
! [A: $i,B: $i] :
( ( v_wt @ B )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Com_Opname ) @ C ) @ v_U ) )
=> ( v_P @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) )
=> ( v_P @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( v_mgt @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(5810,plain,
! [A: $i,B: $i] :
( ( v_wt @ B )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Com_Opname ) @ C ) @ v_U ) )
=> ( v_P @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) )
=> ( v_P @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( v_mgt @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(1161,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ C @ C @ B @ ( c_Fun_Oid @ C ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__o) ).
thf(5659,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ C @ C @ B @ ( c_Fun_Oid @ C ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(3021,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1092,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Obij__betw @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ D ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ B )
= A )
=> ( c_Fun_Obij__betw @ G @ F @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__subset) ).
thf(5437,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Obij__betw @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ D ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ B )
= A )
=> ( c_Fun_Obij__betw @ G @ F @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(774,axiom,
! [A: $i] : ( c_Fun_Oinj__on @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__singleton) ).
thf(4201,plain,
! [A: $i] : ( c_Fun_Oinj__on @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ E ) @ B ) @ A ) ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__INF__iff) ).
thf(2452,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ E ) @ B ) @ A ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ E ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(840,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__single) ).
thf(4447,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1087,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(5422,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__iff) ).
thf(1337,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(32,axiom,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__UNIV) ).
thf(1411,plain,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__lower) ).
thf(5365,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).
thf(4835,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oord @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__iff) ).
thf(1823,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oord @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
=> ( ( ( hAPP @ B @ E )
= ( hAPP @ B @ F ) )
=> ( E = F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
thf(3053,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
=> ( ( ( hAPP @ B @ E )
= ( hAPP @ B @ F ) )
=> ( E = F ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
=> ( ( ( hAPP @ B @ E )
= ( hAPP @ B @ F ) )
=> ( E = F ) ) ) )
=> ( c_Fun_Oinj__on @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(841,axiom,
! [A: $i,B: $i,C: $i] : ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).
thf(4450,plain,
! [A: $i,B: $i,C: $i] : ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(3345,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(846,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__empty) ).
thf(4464,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Int__distrib) ).
thf(2109,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(932,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).
thf(4824,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(2072,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(635,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_OwfP @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
thf(3661,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_OwfP @ B @ A )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ B @ A ) @ C ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ B @ A ) @ C ) )
=> ( c_Wellfounded_OwfP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ B ) @ A )
= ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__def) ).
thf(2412,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ B ) @ A )
= ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(433,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) )
<=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
thf(2876,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ) )
& ( ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(769,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ A @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1__nat) ).
thf(4183,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ A @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
thf(3477,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(644,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).
thf(3698,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(1078,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).
thf(5390,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(2463,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(559,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ B @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
thf(3397,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ B @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).
thf(3830,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1159,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).
thf(5654,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__commute) ).
thf(2595,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(986,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
thf(5028,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(905,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Ovimage @ A @ E @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageI2) ).
thf(4728,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Ovimage @ A @ E @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(146,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(1818,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
thf(6014,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(1096,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
thf(5454,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1276,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(6063,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ B @ C @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Fun_Oid @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__o__cancel) ).
thf(3072,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ B @ C @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Fun_Oid @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(1180,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ E ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ E ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__induct) ).
thf(5718,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ E ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ E ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).
thf(2495,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1028,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
<=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
thf(5173,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(5982,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(1164,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ F @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ E @ D ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ E @ D ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ F @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).
thf(5669,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ F @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ E @ D ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ E @ D ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ F @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(849,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(4479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(1114,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__mono) ).
thf(5501,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(160,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(1855,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(223,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
thf(2077,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( c_Fun_Obij__betw @ G @ C @ B @ D @ A )
<=> ( c_Fun_Obij__betw @ H @ C @ ( hAPP @ ( c_Fun_Ocomp @ G @ C @ H @ B ) @ F ) @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__comp__iff) ).
thf(4037,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( ( c_Fun_Obij__betw @ G @ C @ B @ D @ A )
=> ( c_Fun_Obij__betw @ H @ C @ ( hAPP @ ( c_Fun_Ocomp @ G @ C @ H @ B ) @ F ) @ E @ A ) )
& ( ( c_Fun_Obij__betw @ H @ C @ ( hAPP @ ( c_Fun_Ocomp @ G @ C @ H @ B ) @ F ) @ E @ A )
=> ( c_Fun_Obij__betw @ G @ C @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__is__Un) ).
thf(2976,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(816,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ B ) @ c_Int_OInteg ) )
=> ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ ( hAPP @ c_Int_ORep__Integ @ C ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__induct) ).
thf(4376,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ B ) @ c_Int_OInteg ) )
=> ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ ( hAPP @ c_Int_ORep__Integ @ C ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(542,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding @ D @ C @ B @ A )
=> ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Fun_Oid @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oempty) ).
thf(3317,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding @ D @ C @ B @ A )
=> ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Fun_Oid @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(5168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__left) ).
thf(4500,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(2231,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(685,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(3858,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(4311,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
thf(2644,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I4_J) ).
thf(3905,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ ( hAPP @ D @ ( hAPP @ c_Nat_OSuc @ F ) ) ) @ ( hAPP @ D @ F ) ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ ( hAPP @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ D @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sequence__trans) ).
thf(1522,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ ( hAPP @ D @ ( hAPP @ c_Nat_OSuc @ F ) ) ) @ ( hAPP @ D @ F ) ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ ( hAPP @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ D @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(997,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I10_J) ).
thf(5069,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter__neutral) ).
thf(2395,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Sup__fold__sup) ).
thf(2062,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( c_Fun_Oinj__on @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Equiv__Relations_Oquotient @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ A ) @ B )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__quotient__disjoint) ).
thf(3377,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( c_Fun_Oinj__on @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Equiv__Relations_Oquotient @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ A ) @ B )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( c_Fun_Oinj__on @ E @ B @ A @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) )
<=> ( c_Fun_Oinj__on @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ F @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on__iff) ).
thf(3040,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( c_Fun_Oinj__on @ E @ B @ A @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ F @ A ) @ D ) @ C ) )
& ( ( c_Fun_Oinj__on @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ F @ A ) @ D ) @ C )
=> ( c_Fun_Oinj__on @ E @ B @ A @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ F @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UN) ).
thf(4391,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ F @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(451,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(2953,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__mono) ).
thf(2590,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(1055,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
thf(5297,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(573,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(3460,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(926,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ D @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ E @ B @ ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ A ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__comp) ).
thf(4807,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ D @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ E @ B @ ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ A ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1226,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplD) ).
thf(5878,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).
thf(5625,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(1083,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
thf(5405,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ E @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).
thf(2837,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ E @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(585,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(3498,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ A @ D @ ( hAPP @ ( c_COMBK @ D @ A ) @ C ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ A @ D @ ( hAPP @ ( c_COMBK @ D @ A ) @ C ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__const) ).
thf(4215,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ A @ D @ ( hAPP @ ( c_COMBK @ D @ A ) @ C ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ A @ D @ ( hAPP @ ( c_COMBK @ D @ A ) @ C ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(1971,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def) ).
thf(1793,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(827,axiom,
! [A: $i,B: $i] : ( c_Fun_Obij__betw @ B @ B @ ( c_Fun_Oid @ B ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__id) ).
thf(4408,plain,
! [A: $i,B: $i] : ( c_Fun_Obij__betw @ B @ B @ ( c_Fun_Oid @ B ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(1267,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Com_Opname ) @ A ) @ v_U ) )
=> ( v_wt @ ( c_Option_Othe @ tc_Com_Ocom @ ( c_Com_Obody @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I4_J) ).
thf(6031,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Com_Opname ) @ A ) @ v_U ) )
=> ( v_wt @ ( c_Option_Othe @ tc_Com_Ocom @ ( c_Com_Obody @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(1068,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__iff) ).
thf(5348,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(1262,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__rec @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(6017,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__rec @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(912,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(4747,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(876,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert__iff) ).
thf(4592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I1_J) ).
thf(3429,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I4_J) ).
thf(4739,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__f) ).
thf(3365,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaI) ).
thf(2316,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1284,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__empty @ B ) @ A )
= ( c_Lazy__Sequence_Oempty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
thf(6089,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__empty @ B ) @ A )
= ( c_Lazy__Sequence_Oempty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(2141,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(1176,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int__subset) ).
thf(5701,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(837,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__card__le__card__Diff) ).
thf(4440,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I4_J) ).
thf(2901,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1153,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ I @ H @ G @ F ) @ E )
= ( hAPP @ ( c_Fun_Ocomp @ D @ H @ G @ C ) @ B ) )
=> ( ( hAPP @ F @ ( hAPP @ E @ A ) )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(5636,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ I @ H @ G @ F ) @ E )
= ( hAPP @ ( c_Fun_Ocomp @ D @ H @ G @ C ) @ B ) )
=> ( ( hAPP @ F @ ( hAPP @ E @ A ) )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ D ) ) @ c_FunDef_Opair__less ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ C ) ) @ c_FunDef_Omax__strict ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ A ) ) @ C ) ) @ c_FunDef_Omax__strict ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__insertI) ).
thf(2042,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ D ) ) @ c_FunDef_Opair__less ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ C ) ) @ c_FunDef_Omax__strict ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ A ) ) @ C ) ) @ c_FunDef_Omax__strict ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofun__left__comm @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ C ) @ B ) ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ C ) @ B ) )
=> ~ ! [H: $i] :
( ( A
= ( hAPP @ ( hAPP @ E @ C ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ B ) @ H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).
thf(1705,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofun__left__comm @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ C ) @ B ) ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ C ) @ B ) )
=> ~ ! [H: $i] :
( ( A
= ( hAPP @ ( hAPP @ E @ C ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ B ) @ H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imp__bij__betw) ).
thf(4543,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(1247,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
thf(5967,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(1426,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ F @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__INT) ).
thf(3530,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ F @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(743,axiom,
! [A: $i] :
( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) @ c_FunDef_Omin__strict ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__emptyI) ).
thf(4090,plain,
! [A: $i] :
( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) @ c_FunDef_Omin__strict ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__constant) ).
thf(1655,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).
thf(4011,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(3649,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Hilbert__Choice_Oinv__into @ B @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__inv__eq) ).
thf(4026,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Hilbert__Choice_Oinv__into @ B @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(1052,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert__distrib) ).
thf(5288,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1867,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(2184,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__idemp) ).
thf(4638,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1019,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ B @ A ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oclosed) ).
thf(5146,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ B @ A ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__constant) ).
thf(1872,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(1919,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ B ) ) @ ( hAPP @ D @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ A ) ) @ ( hAPP @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp) ).
thf(3253,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ B ) ) @ ( hAPP @ D @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ A ) ) @ ( hAPP @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ? [E: $i] : ( c_Fun_Obij__betw @ D @ B @ E @ C @ A )
<=> ( ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BIJ) ).
thf(5161,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( ? [E: $i] : ( c_Fun_Obij__betw @ D @ B @ E @ C @ A )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) )
& ( ( ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) )
=> ? [E: $i] : ( c_Fun_Obij__betw @ D @ B @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(798,axiom,
! [A: $i] :
( ( c_Hilbert__Choice_Oinv__into @ A @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Fun_Oid @ A ) )
= ( c_Fun_Oid @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__id) ).
thf(4294,plain,
! [A: $i] :
( ( c_Hilbert__Choice_Oinv__into @ A @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Fun_Oid @ A ) )
= ( c_Fun_Oid @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(788,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Set_Ovimage @ F @ D @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ E @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__compose) ).
thf(4247,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Set_Ovimage @ F @ D @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ E @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(606,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).
thf(3562,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(243,axiom,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__empty) ).
thf(2146,plain,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(975,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(4980,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
thf(1507,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(2360,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(1746,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(152,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc__greaterThan) ).
thf(1835,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(625,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(3629,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
thf(5740,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
thf(2046,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(1914,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(137,axiom,
! [A: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).
thf(1782,plain,
! [A: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(3502,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(1187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( C
= ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(5745,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( C
= ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(1238,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(5921,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).
thf(4198,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Diff) ).
thf(3140,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ B ) ) @ A ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ B @ F ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__le__iff) ).
thf(1366,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ B ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ B @ F ) ) @ A ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1288,axiom,
( ( hAPP @ ( c_Finite__Set_Ocard @ t_a ) @ v_G )
= ( hAPP @ ( c_Finite__Set_Ocard @ t_a ) @ ( hAPP @ ( c_Set_Oimage @ tc_Com_Opname @ t_a @ v_mgt__call ) @ v_U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(6102,plain,
( ( hAPP @ ( c_Finite__Set_Ocard @ t_a ) @ v_G )
= ( hAPP @ ( c_Finite__Set_Ocard @ t_a ) @ ( hAPP @ ( c_Set_Oimage @ tc_Com_Opname @ t_a @ v_mgt__call ) @ v_U ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(1049,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
<=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(5269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(172,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
thf(1904,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(4467,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__idem @ E @ D @ C @ B )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__comp) ).
thf(3597,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__idem @ E @ D @ C @ B )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(1148,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryE) ).
thf(5621,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
thf(5024,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(819,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__image__vimage__eq) ).
thf(4386,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(27,axiom,
! [A: $i] :
( ( hAPP @ ( c_Relation_OField @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__empty) ).
thf(1391,plain,
! [A: $i] :
( ( hAPP @ ( c_Relation_OField @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(1576,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_Set_Oinsert @ B ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__fold__image) ).
thf(3730,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_Set_Oinsert @ B ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(1181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD1) ).
thf(5723,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
thf(4916,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(1234,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__upper) ).
thf(5903,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ C ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(1359,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__apply) ).
thf(1601,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__subset) ).
thf(3466,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(1056,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterD) ).
thf(5301,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(2400,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(971,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN) ).
thf(4963,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
thf(2067,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(190,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1967,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(1709,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(863,axiom,
! [A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__empty) ).
thf(4524,plain,
! [A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq) ).
thf(3195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UN) ).
thf(3644,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I2_J) ).
thf(3275,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetD) ).
thf(4151,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(781,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ c_Int_OInteg ) )
=> ~ ! [B: $i] :
( A
!= ( hAPP @ c_Int_ORep__Integ @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__cases) ).
thf(4224,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ c_Int_OInteg ) )
=> ~ ! [B: $i] :
( A
!= ( hAPP @ c_Int_ORep__Integ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(4761,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).
thf(2708,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I5_J) ).
thf(3776,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ C ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ B ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp) ).
thf(4349,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ C ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ B ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Wellfounded_Omax__ext @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__wf) ).
thf(1455,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Wellfounded_Omax__ext @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib2) ).
thf(1832,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__vimage__eq__inv__image) ).
thf(3820,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
thf(5553,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( c_Finite__Set_Ofun__left__comm @ B @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ D ) @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).
thf(1628,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( c_Finite__Set_Ofun__left__comm @ B @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ D ) @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(785,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I4_J) ).
thf(4238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(4539,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(2698,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(1760,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1228,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb2) ).
thf(5883,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton__if) ).
thf(3046,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I9_J) ).
thf(3689,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__union @ D @ C @ B ) @ A )
= ( c_Lazy__Sequence_Oappend @ D @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__union__def) ).
thf(6095,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__union @ D @ C @ B ) @ A )
= ( c_Lazy__Sequence_Oappend @ D @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(1192,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__iff) ).
thf(5759,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
& ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(1907,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
& ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ A ) @ D ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
thf(2501,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ A ) @ D ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(1277,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ B @ ( c_COMBI @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
thf(6066,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ B @ ( c_COMBI @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(1511,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(581,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc) ).
thf(3485,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ A @ D ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__no__infinite__down__chainE) ).
thf(2682,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ A @ D ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
thf(1826,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1154,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
thf(5640,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ B @ ( hAPP @ ( c_COMBK @ B @ E ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant) ).
thf(3089,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ B @ ( hAPP @ ( c_COMBK @ B @ E ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
thf(1992,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(551,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
thf(3353,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(670,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ( c_Fun_Oinj__on @ E @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).
thf(3803,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ( c_Fun_Oinj__on @ E @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(2466,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
thf(4428,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(478,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(3043,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
<=> ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__insert) ).
thf(2745,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Owf @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
=> ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) )
& ( ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
=> ( c_Wellfounded_Owf @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ B ) @ A ) ) @ A ) )
=> ( ( hAPP @ ( c_Relation_OImage @ C @ C @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).
thf(2571,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ B ) @ A ) ) @ A ) )
=> ( ( hAPP @ ( c_Relation_OImage @ C @ C @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hAPP @ ( hAPP @ D @ C ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
thf(1800,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hAPP @ ( hAPP @ D @ C ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(750,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
thf(4119,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ A ) ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect) ).
thf(1479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(934,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__diff) ).
thf(4830,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Oinj__on @ B @ E @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ D @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ B @ C ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__comp) ).
thf(4141,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Oinj__on @ B @ E @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ D @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ B @ C ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Un) ).
thf(4793,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(972,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffE) ).
thf(4967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ? [C: $i] : ( c_Fun_Obij__betw @ tc_Nat_Onat @ B @ C @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__bij__betw__nat__finite) ).
thf(1847,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ? [C: $i] : ( c_Fun_Obij__betw @ tc_Nat_Onat @ B @ C @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1042,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(5231,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(314,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(2420,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__fold__remove) ).
thf(3840,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(1044,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ D ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__injective) ).
thf(5256,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ D ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(811,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__idem @ G @ F @ E @ D )
=> ( ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).
thf(4353,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__idem @ G @ F @ E @ D )
=> ( ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1223,axiom,
! [A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ A @ ( c_Fun_Oid @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__id) ).
thf(5866,plain,
! [A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ A @ ( c_Fun_Oid @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(1038,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__anti__mono) ).
thf(5214,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(1143,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ D @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
thf(5605,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ D @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ! [F: $i,G: $i] :
( ( hAPP @ B @ ( hAPP @ ( hAPP @ D @ F ) @ G ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ B @ F ) ) @ ( hAPP @ B @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ ( hAPP @ ( c_Set_Oimage @ E @ E @ B ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
thf(4862,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ! [F: $i,G: $i] :
( ( hAPP @ B @ ( hAPP @ ( hAPP @ D @ F ) @ G ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ B @ F ) ) @ ( hAPP @ B @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ ( hAPP @ ( c_Set_Oimage @ E @ E @ B ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Ointros) ).
thf(4788,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oremove) ).
thf(2169,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(62,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
thf(1514,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(768,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(4179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(1033,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__iff) ).
thf(5193,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Un__distrib1) ).
thf(2373,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(1347,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) )
& ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(3919,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(1061,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ A @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__anti__mono) ).
thf(5323,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ A @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(961,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__mono) ).
thf(4928,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(993,axiom,
! [A: $i,B: $i] :
( ( v_P @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ B ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( v_mgt @ ( c_Option_Othe @ tc_Com_Ocom @ ( c_Com_Obody @ B ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) )
=> ( v_P @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I2_J) ).
thf(5052,plain,
! [A: $i,B: $i] :
( ( v_P @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ B ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( v_mgt @ ( c_Option_Othe @ tc_Com_Ocom @ ( c_Com_Obody @ B ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) )
=> ( v_P @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(892,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ B ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ B @ C ) @ A ) ) @ ( c_Product__Type_OPair @ D @ C ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__eta) ).
thf(4675,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ B ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ B @ C ) @ A ) ) @ ( c_Product__Type_OPair @ D @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(3312,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1217,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
thf(5851,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(1931,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(3951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(247,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__singleton) ).
thf(2158,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(1287,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ G @ F @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ E @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(6098,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ G @ F @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ E @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(883,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Obij__betw @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ F @ B @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) ) @ A )
= ( hAPP @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__inv__into__eq) ).
thf(4632,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Obij__betw @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ F @ B @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) ) @ A )
= ( hAPP @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__UN) ).
thf(5727,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
thf(1641,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(645,axiom,
! [A: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
thf(3708,plain,
! [A: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(281,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(2301,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton) ).
thf(1815,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I6_J) ).
thf(2989,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SUPI) ).
thf(1362,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__vimage__image__eq) ).
thf(2852,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(522,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__bottom) ).
thf(3231,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(800,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
thf(4302,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_OwfP @ B @ A )
<=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__def) ).
thf(2388,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_OwfP @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) )
& ( ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) )
=> ( c_Wellfounded_OwfP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(687,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__less) ).
thf(3866,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(419,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(2829,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I1_J) ).
thf(3788,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int2) ).
thf(2456,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(1946,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__insert) ).
thf(3524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ D @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Union) ).
thf(2090,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ D @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(23,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__le__nat) ).
thf(1373,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD2) ).
thf(1911,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product) ).
thf(1682,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_Set_OPow @ D ) ) @ A ) ) ) @ ( hAPP @ ( c_Set_OPow @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Pow__subset) ).
thf(2925,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_Set_OPow @ D ) ) @ A ) ) ) @ ( hAPP @ ( c_Set_OPow @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(1237,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
thf(5914,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(1023,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).
thf(5156,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ D @ B ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__const) ).
thf(2254,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ D @ B ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Wellfounded_Oacc @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
thf(2335,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Wellfounded_Oacc @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(897,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint2) ).
thf(4696,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofun__left__comm @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ C ) )
=> ? [H: $i] :
( ( B
= ( hAPP @ ( hAPP @ E @ A ) @ H ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) @ H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).
thf(4205,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofun__left__comm @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ C ) )
=> ? [H: $i] :
( ( B
= ( hAPP @ ( hAPP @ E @ A ) @ H ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) @ H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(978,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__def) ).
thf(4988,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(1047,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
thf(5264,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(1257,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
thf(6002,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(1230,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
<=> ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(5888,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
=> ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) ) )
& ( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( c_Fun_Oinj__on @ D @ ( tc_prod @ C @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_prod @ C @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).
thf(4173,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( c_Fun_Oinj__on @ D @ ( tc_prod @ C @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_prod @ C @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(702,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
thf(3934,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B ) ) )
=> ( c_Fun_Oinj__on @ C @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
thf(5084,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B ) ) )
=> ( c_Fun_Oinj__on @ C @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__leI) ).
thf(2105,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(739,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(4072,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).
thf(1450,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I8_J) ).
thf(3075,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff__insert) ).
thf(5597,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(97,axiom,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__empty) ).
thf(1632,plain,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(799,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ E ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Inter) ).
thf(4297,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ E ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(326,axiom,
c_Wellfounded_Owf @ tc_Nat_Onat @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__less) ).
thf(2469,plain,
c_Wellfounded_Owf @ tc_Nat_Onat @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert) ).
thf(4733,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).
thf(2259,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).
thf(4001,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__E) ).
thf(4820,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__Pow__eq) ).
thf(3163,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).
thf(2650,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__binary) ).
thf(1334,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton) ).
thf(3527,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).
thf(5558,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ B ) ) ) ) )
=> ( B
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
thf(1864,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ B ) ) ) ) )
=> ( B
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD1) ).
thf(1677,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
thf(2034,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
<=> ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__Un) ).
thf(4871,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) )
& ( ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(1016,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( C = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
thf(5135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( C = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(923,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__Diff1) ).
thf(4798,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ D )
= A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__partition) ).
thf(4556,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ D )
= A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntI) ).
thf(5259,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(662,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(3771,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(683,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(3851,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV2) ).
thf(1447,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(672,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(3808,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
thf(1345,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OImage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__empty) ).
thf(1433,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OImage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(5665,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I8_J) ).
thf(4707,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C )
= B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
thf(5328,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C )
= B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(1248,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN__I) ).
thf(5970,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) )
<=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
thf(1696,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) )
& ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
| ( B
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).
thf(5695,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
| ( B
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ImageE) ).
thf(1928,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1196,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset) ).
thf(5773,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(1082,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
thf(5401,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Un) ).
thf(2281,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(5643,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(566,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
thf(3421,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Ofun__upd @ D @ C @ B @ A @ ( hAPP @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(1622,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Ofun__upd @ D @ C @ B @ A @ ( hAPP @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(742,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ D @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__eq__UN) ).
thf(4087,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ D @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__less__ub) ).
thf(2979,plain,
! [A: $i,B: $i] :
( ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ G @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ C ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
thf(1394,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ G @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ C ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I7_J) ).
thf(3157,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1216,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
<=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__iff) ).
thf(5846,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(240,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(2137,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
thf(5321,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(4307,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(731,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).
thf(4040,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(201,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(2002,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int) ).
thf(3955,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__def) ).
thf(4643,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
& ( ( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(1943,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(613,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Diff) ).
thf(3588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(797,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un) ).
thf(4285,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
& ( ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(619,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq) ).
thf(3606,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(1210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H) ).
thf(5824,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__seg__image__imp__finite) ).
thf(4588,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(877,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(4604,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I2_J) ).
thf(3450,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(614,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I8_J) ).
thf(3591,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I2_J) ).
thf(3301,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(1691,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1272,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__not__random__dseq @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__not__seq @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(6047,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__not__random__dseq @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__not__seq @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Wellfounded_Owf @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__subset) ).
thf(2164,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Wellfounded_Owf @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(1018,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
thf(5142,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1053,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( hAPP @ E @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI) ).
thf(5291,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( hAPP @ E @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
thf(2093,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__eq__subset__Compl) ).
thf(3679,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(88,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
thf(1604,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(444,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(2922,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(1245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(5961,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Wellfounded_Oacc @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
thf(2011,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Owf @ B @ A )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Wellfounded_Oacc @ B @ A ) ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Wellfounded_Oacc @ B @ A ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ F ) )
=> ( c_Fun_Oinj__on @ D @ C @ B @ ( hAPP @ A @ G ) ) )
=> ( c_Fun_Oinj__on @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__INTER) ).
thf(3097,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ F ) )
=> ( c_Fun_Oinj__on @ D @ C @ B @ ( hAPP @ A @ G ) ) )
=> ( c_Fun_Oinj__on @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1263,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Oneg__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Oneg__single @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__single__def) ).
thf(6020,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Oneg__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Oneg__single @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(1189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__empty @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__empty @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__empty__def) ).
thf(5751,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__empty @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__empty @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( ( hAPP @ A @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__0__iff) ).
thf(2574,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( ( hAPP @ A @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( ( hAPP @ A @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(1084,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__iff) ).
thf(5411,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Oone__class_Oone @ D ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ D ) ) @ B )
= ( c_Groups_Oone__class_Oone @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__1) ).
thf(1306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Oone__class_Oone @ D ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ D ) ) @ B )
= ( c_Groups_Oone__class_Oone @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(984,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left) ).
thf(5017,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(1311,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1221,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
thf(5862,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(225,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(2083,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I6_J) ).
thf(4031,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(736,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq2) ).
thf(4059,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(302,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
thf(2382,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__upper) ).
thf(2773,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1051,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__if) ).
thf(5281,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
thf(4999,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) @ F ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I2) ).
thf(5122,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) @ F ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(565,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__f__f) ).
thf(3418,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(960,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
thf(4925,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(1285,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ B @ ( c_Fun_Oid @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__id) ).
thf(6092,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ B @ ( c_Fun_Oid @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(310,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
thf(2409,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(1723,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
thf(3827,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(1256,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(6000,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Int__subset) ).
thf(4397,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Un) ).
thf(4434,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oinsert__idem) ).
thf(5044,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(1048,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
thf(5266,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(1666,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(862,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) ) )
=> ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff__nat) ).
thf(4521,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) ) )
=> ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(3233,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE2) ).
thf(2606,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
thf(3154,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
thf(3339,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ B ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
thf(1343,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ B ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OField @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A ) )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Relation_OField @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Union) ).
thf(2560,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OField @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A ) )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Relation_OField @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(712,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ C ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__fold__insert) ).
thf(3972,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ C ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__subset) ).
thf(1502,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Set_Oinsert @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__def) ).
thf(1751,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Set_Oinsert @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1208,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).
thf(5815,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(1190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I5_J) ).
thf(5754,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(1619,plain,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(1370,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1007,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ C @ B @ C @ A ) @ ( c_Fun_Oid @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__id) ).
thf(5102,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ C @ B @ C @ A ) @ ( c_Fun_Oid @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
thf(2986,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__cancel) ).
thf(3250,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Collect__eq) ).
thf(2132,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OPow @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__not__empty) ).
thf(2890,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OPow @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( ( hAPP @ ( c_Fun_Ocomp @ C @ B @ B @ A ) @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( c_Fun_Oid @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff) ).
thf(4160,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ C @ B @ B @ A ) @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( c_Fun_Oid @ B ) ) )
& ( ( ( hAPP @ ( c_Fun_Ocomp @ C @ B @ B @ A ) @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( c_Fun_Oid @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(2528,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__right) ).
thf(3471,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( ( hAPP @ ( c_Fun_Ocomp @ B @ C @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Fun_Oid @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__iff) ).
thf(4044,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ B @ C @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Fun_Oid @ C ) ) )
& ( ( ( hAPP @ ( c_Fun_Ocomp @ B @ C @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Fun_Oid @ C ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__insert) ).
thf(3286,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(1215,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
thf(5843,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__equiv__class) ).
thf(1883,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(1560,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(706,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).
thf(3948,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(318,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(2433,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__eq__Inter) ).
thf(3137,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1172,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Inter) ).
thf(5690,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(1098,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
thf(5460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Omax__extp @ D @ C @ B @ A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).
thf(4327,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Omax__extp @ D @ C @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(1127,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
thf(5551,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(1275,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).
thf(6060,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__inter) ).
thf(3028,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(1219,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) )
=> ( ( c_Fun_Oinj__on @ C @ D @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
thf(5858,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) )
=> ( ( c_Fun_Oinj__on @ C @ D @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(401,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(2741,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__imp__surj) ).
thf(4461,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(1194,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).
thf(5769,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(3958,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(512,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(3191,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(796,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(4280,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__I) ).
thf(5492,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq2) ).
thf(3618,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
thf(2628,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(771,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__absorb) ).
thf(4192,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(383,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
thf(2670,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(74,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
thf(1555,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
thf(2332,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(418,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).
thf(2826,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).
thf(2820,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(168,axiom,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__UNIV) ).
thf(1888,plain,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(4,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(1296,plain,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Oinj__on @ G @ F @ E @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) )
=> ( ( c_Fun_Oinj__on @ D @ G @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) ) ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ D @ E ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ G @ D @ F @ ( c_Hilbert__Choice_Oinv__into @ D @ G @ B @ C ) ) @ ( c_Hilbert__Choice_Oinv__into @ G @ F @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) @ E ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__comp) ).
thf(4553,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Oinj__on @ G @ F @ E @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) )
=> ( ( c_Fun_Oinj__on @ D @ G @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) ) ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ D @ E ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ G @ D @ F @ ( c_Hilbert__Choice_Oinv__into @ D @ G @ B @ C ) ) @ ( c_Hilbert__Choice_Oinv__into @ G @ F @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) @ E ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI2) ).
thf(5534,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Inf__iff) ).
thf(1687,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(1457,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(259,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(2200,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_prod @ H @ G ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ H @ G ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ G @ tc_HOL_Obool ) @ H ) @ C ) ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ H @ ( tc_fun @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( tc_fun @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( tc_fun @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) ) @ H ) @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ H ) @ ( c_Product__Type_OSigma @ F @ E ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ G ) @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) ) @ A ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Times__distrib) ).
thf(2609,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_prod @ H @ G ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ H @ G ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ G @ tc_HOL_Obool ) @ H ) @ C ) ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ H @ ( tc_fun @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( tc_fun @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( tc_fun @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) ) @ H ) @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ H ) @ ( c_Product__Type_OSigma @ F @ E ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ G ) @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) ) @ A ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(825,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I9_J) ).
thf(4402,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(1011,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(5113,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ B ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__add__Un) ).
thf(2181,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ B ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(965,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
thf(4942,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(3647,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
<=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty) ).
thf(2112,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Oone__class_Oone @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__one) ).
thf(1291,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Oone__class_Oone @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(803,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(4316,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(996,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ C ) @ F ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2CI) ).
thf(5066,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ C ) @ F ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(1178,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterE) ).
thf(5714,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Un__distrib) ).
thf(2840,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) )
<=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).
thf(1772,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) )
=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
thf(1804,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1201,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ C @ A ) ) @ ( c_Wellfounded_Oaccp @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__subset) ).
thf(5798,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ C @ A ) ) @ ( c_Wellfounded_Oaccp @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__subset) ).
thf(1587,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C )
<=> ( ( hAPP @ C @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(2631,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C )
=> ( ( hAPP @ C @ B )
= A ) )
& ( ( ( hAPP @ C @ B )
= A )
=> ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(962,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnCI) ).
thf(4930,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(374,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(2638,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(571,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).
thf(3440,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ) )
& ( ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1104,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).
thf(5475,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(1031,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__top) ).
thf(5189,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(1592,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(337,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(2498,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__Compl__image__subset) ).
thf(3782,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__compl) ).
thf(3615,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
thf(3482,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(1040,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__is__image) ).
thf(5221,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Omax__extp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) @ B @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).
thf(2377,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Omax__extp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ D @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ D @ C ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(2801,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__mult @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ B @ G ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ E @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ F @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) ) @ E ) @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ ( tc_prod @ E @ C ) @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ C @ F ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ C ) @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Sigma) ).
thf(1953,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__mult @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ B @ G ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ E @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ F @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) ) @ E ) @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ ( tc_prod @ E @ C ) @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ C @ F ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ C ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(981,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
thf(5006,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).
thf(1375,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).
thf(2973,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__image__Compl__eq) ).
thf(4486,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ E @ D @ C )
=> ( ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
thf(2509,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ E @ D @ C )
=> ( ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(493,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(3102,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(1088,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
thf(5428,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(109,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(1672,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Obij__betw @ G @ F @ E @ D @ C )
=> ( ( c_Fun_Obij__betw @ G @ F @ E @ B @ A )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ G @ F @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__combine) ).
thf(3518,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Obij__betw @ G @ F @ E @ D @ C )
=> ( ( c_Fun_Obij__betw @ G @ F @ E @ B @ A )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ G @ F @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(1135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Quotient_OBabs @ E @ B @ C @ A ) @ D )
= ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Babs__def) ).
thf(5583,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Quotient_OBabs @ E @ B @ C @ A ) @ D )
= ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ C @ ( c_Fun_Oid @ C ) @ B @ A )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__id__iff) ).
thf(3632,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Fun_Obij__betw @ C @ C @ ( c_Fun_Oid @ C ) @ B @ A )
=> ( B = A ) )
& ( ( B = A )
=> ( c_Fun_Obij__betw @ C @ C @ ( c_Fun_Oid @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(656,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(3746,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(938,axiom,
v_wt @ v_c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(4840,plain,
v_wt @ v_c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff) ).
thf(3078,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(697,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff) ).
thf(3916,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(705,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
<=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
thf(3941,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) ) )
& ( ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ C ) ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Union__image) ).
thf(3018,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ C ) ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
thf(4898,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ C ) @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__empty) ).
thf(1397,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ C ) @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(793,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I1_J) ).
thf(4263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(1567,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(968,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__is__empty) ).
thf(4951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).
thf(3143,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(999,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ D @ C ) ) @ ( hAPP @ ( c_Set_OPow @ E ) @ B ) )
= ( hAPP @ ( c_Set_OPow @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__surj) ).
thf(5075,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ D @ C ) ) @ ( hAPP @ ( c_Set_OPow @ E ) @ B ) )
= ( hAPP @ ( c_Set_OPow @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(1112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
thf(5496,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(820,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__wfPD) ).
thf(4389,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(908,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__eq) ).
thf(4736,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert) ).
thf(3573,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(865,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ E ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__empty__induct) ).
thf(4530,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ E ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(1242,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
thf(5941,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(1212,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
<=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
thf(5830,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) ) ) )
& ( ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(861,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__right) ).
thf(4518,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1025,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ D @ C @ tc_HOL_Obool @ E ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryI) ).
thf(5166,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ D @ C @ tc_HOL_Obool @ E ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(1209,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__iff) ).
thf(5818,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty1) ).
thf(1964,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(466,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition) ).
thf(3000,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(2323,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(976,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplI) ).
thf(4983,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(1029,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnionD) ).
thf(5181,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(561,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__Compl__subset) ).
thf(3407,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) )
<=> ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ C ) )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
thf(4772,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) )
=> ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ C ) )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) ) )
& ( ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ C ) )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) )
=> ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ F ) @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ D ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib2) ).
thf(3094,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ F ) @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ D ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(764,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).
thf(4167,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(49,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
thf(1461,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(4421,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
thf(1424,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1100,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2E) ).
thf(5464,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(871,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= A ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I2_J) ).
thf(4545,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= A ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ B @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) ) @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fold__sup) ).
thf(2080,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ B @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) ) @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(1199,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).
thf(5786,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(33,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
<=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(1414,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) )
& ( ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__nat) ).
thf(1842,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
thf(5588,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofun__left__comm @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).
thf(1584,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofun__left__comm @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(860,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(4513,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subset__eq) ).
thf(4744,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(1937,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_Relation_OImage @ B @ B @ A ) @ C ) ) )
=> ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfI__pf) ).
thf(2172,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_Relation_OImage @ B @ B @ A ) @ C ) ) )
=> ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( c_Fun_Oinj__on @ B @ D @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Ovimage @ B @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageI) ).
thf(4054,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( c_Fun_Oinj__on @ B @ D @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Ovimage @ B @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(1162,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
thf(5662,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ ( hAPP @ ( c_COMBK @ B @ C ) @ A ) ) @ D )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ ( hAPP @ ( c_COMBK @ B @ C ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant__conv) ).
thf(2349,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ ( hAPP @ ( c_COMBK @ B @ C ) @ A ) ) @ D )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ ( hAPP @ ( c_COMBK @ B @ C ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(947,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
thf(4867,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Pow__eq) ).
thf(4444,plain,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(1235,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
thf(5905,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(603,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
thf(3555,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__finite__eq) ).
thf(1644,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Un) ).
thf(4814,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C )
= A )
<=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
thf(1612,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) )
& ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(2472,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(879,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ B @ E @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( c_Hilbert__Choice_Oinv__into @ B @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ B @ C ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ B @ D @ ( c_Hilbert__Choice_Oinv__into @ B @ E @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__inv__distrib) ).
thf(4621,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ B @ E @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( c_Hilbert__Choice_Oinv__into @ B @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ B @ C ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ B @ D @ ( c_Hilbert__Choice_Oinv__into @ B @ E @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(925,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ B @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
thf(4804,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ B @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__E) ).
thf(5576,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__Int) ).
thf(1297,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(1974,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(357,axiom,
( ( c_Orderings_Obot__class_Obot @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__nat__def) ).
thf(2581,plain,
( ( c_Orderings_Obot__class_Obot @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1169,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__into) ).
thf(5683,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(1984,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff__nat) ).
thf(3333,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ A ) )
=> ( F = G ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).
thf(4416,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ A ) )
=> ( F = G ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(4846,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) @ F )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(3611,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) @ F )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
thf(2519,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(5481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(1075,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(5374,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(1020,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
thf(5149,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(1268,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__case @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(6033,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__case @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(68,axiom,
! [A: $i] : ( c_Wellfounded_Owf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__empty) ).
thf(1530,plain,
! [A: $i] : ( c_Wellfounded_Owf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
thf(1539,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
thf(2487,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(2598,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(973,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__UNIV) ).
thf(4970,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__Int__eq) ).
thf(3743,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1249,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).
thf(5973,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__finite) ).
thf(4244,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Compl) ).
thf(3222,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(599,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(3540,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(202,axiom,
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__atLeast__UNIV) ).
thf(2006,plain,
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert__remove) ).
thf(2566,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(703,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff) ).
thf(3937,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Typedef_Otype__definition @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__range) ).
thf(5766,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Typedef_Otype__definition @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(783,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).
thf(4231,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
thf(1852,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(2813,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) )
& ( ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ D ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__fold__inf) ).
thf(3115,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ D ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(5305,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__subset__Int) ).
thf(3247,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_prod @ H @ G ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ C @ F ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ H @ G ) @ F @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ F ) @ E ) ) ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__twice) ).
thf(3409,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_prod @ H @ G ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ C @ F ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ H @ G ) @ F @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ F ) @ E ) ) ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(755,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(4135,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ C )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).
thf(3692,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ C )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oneutral) ).
thf(2052,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(86,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(1599,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(954,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ G @ E @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ C @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ C @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(4902,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ G @ E @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ C @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ C @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( c_Fun_Ofun__upd @ E @ G @ C @ B @ A ) )
= ( c_Fun_Ofun__upd @ E @ F @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C ) @ B @ ( hAPP @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__comp) ).
thf(1720,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( c_Fun_Ofun__upd @ E @ G @ C @ B @ A ) )
= ( c_Fun_Ofun__upd @ E @ F @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C ) @ B @ ( hAPP @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).
thf(4259,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
thf(3109,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ B ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ G ) @ ( hAPP @ A @ F ) ) )
=> ( C
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ F ) @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE) ).
thf(1979,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ B ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ G ) @ ( hAPP @ A @ F ) ) )
=> ( C
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ F ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oord @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__iff) ).
thf(2370,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oord @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(1106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__D) ).
thf(5479,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(1027,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).
thf(5170,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(2203,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Ovimage @ B @ B @ ( c_COMBI @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__ident) ).
thf(3225,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Ovimage @ B @ B @ ( c_COMBI @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(4212,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(848,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ F ) @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ D ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib2) ).
thf(4476,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ F ) @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ D ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(1259,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Set_Oimage @ F @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__UN) ).
thf(6011,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Set_Oimage @ F @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un__distrib) ).
thf(1663,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(2617,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(722,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__absorb) ).
thf(4004,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).
thf(2423,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I6_J) ).
thf(2909,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).
thf(3755,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(866,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) @ A )
=> ( c_Fun_Oinj__on @ D @ E @ C @ ( hAPP @ ( c_Set_Oimage @ F @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI) ).
thf(4535,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) @ A )
=> ( c_Fun_Oinj__on @ D @ E @ C @ ( hAPP @ ( c_Set_Oimage @ F @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(349,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(2546,plain,
! [A: $i] :
( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(772,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Set_Oimage @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Union) ).
thf(4195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Set_Oimage @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib1) ).
thf(1779,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(1003,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ F @ F @ E @ ( c_Fun_Oid @ F ) ) @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__id__dest) ).
thf(5090,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ F @ F @ E @ ( c_Fun_Oid @ F ) ) @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ B ) @ A ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfE__pf) ).
thf(2057,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ B ) @ A ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(1712,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(720,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(3999,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ! [D: $i] :
( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ D ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).
thf(2963,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ! [D: $i] :
( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ D ) )
= D ) )
& ( ! [D: $i] :
( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ D ) )
= D )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1184,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D1) ).
thf(5737,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ D ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__product) ).
thf(2368,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(1086,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Typedef_Otype__definition @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ E @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__image) ).
thf(5419,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Typedef_Otype__definition @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ E @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__triv) ).
thf(3639,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(1085,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).
thf(5417,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) )
<=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__empty) ).
thf(2221,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(2189,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(464,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
thf(2995,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1014,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
thf(5126,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(1214,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I10_J) ).
thf(5840,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ D ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
thf(4995,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ D ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Relation_OField @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Field) ).
thf(1732,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Relation_OField @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1167,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(5679,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(958,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionE) ).
thf(4919,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(2176,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).
thf(1754,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
thf(2585,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(1050,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ( hAPP @ K @ ( hAPP @ J @ I ) )
= ( hAPP @ H @ ( hAPP @ G @ F ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ C @ K ) @ J ) @ I )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ B @ D @ A @ H ) @ G ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(5278,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ( hAPP @ K @ ( hAPP @ J @ I ) )
= ( hAPP @ H @ ( hAPP @ G @ F ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ C @ K ) @ J ) @ I )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ B @ D @ A @ H ) @ G ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).
thf(3491,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ A )
=> ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ E @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
thf(3262,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ A )
=> ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ E @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(537,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
thf(3289,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1144,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
<=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(5608,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) ) )
& ( ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) )
=> ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(1121,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__left) ).
thf(5525,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ( c_Fun_Oinj__on @ G @ G @ B @ C )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( c_Set_Oimage @ G @ G @ B ) @ C ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ ( c_Fun_Ocomp @ G @ H @ G @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oreindex) ).
thf(3686,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ( c_Fun_Oinj__on @ G @ G @ B @ C )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( c_Set_Oimage @ G @ G @ B ) @ C ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ ( c_Fun_Ocomp @ G @ H @ G @ A ) @ B ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(853,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).
thf(4489,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Wellfounded_Omeasure @ D ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
thf(2894,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Wellfounded_Omeasure @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Wellfounded_Omeasure @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
thf(2121,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(266,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(2235,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__Field) ).
thf(2144,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(1274,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(6053,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ E @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__inv__into) ).
thf(4131,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ E @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(1265,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Oneg__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Ohb__single @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
thf(6026,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Oneg__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Ohb__single @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite__subset) ).
thf(1680,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1205,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
thf(5808,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(749,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageD) ).
thf(4116,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__is__surj) ).
thf(3871,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ D ) @ C ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ D ) @ C ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__times__insert) ).
thf(2149,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ D ) @ C ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ D ) @ C ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Obij__betw @ F @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Set_Oimage @ F @ E @ D ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__image__INT) ).
thf(3257,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Obij__betw @ F @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Set_Oimage @ F @ E @ D ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oacc @ C @ A ) ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__subset) ).
thf(2717,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oacc @ C @ A ) ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__singleton) ).
thf(1548,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I9_J) ).
thf(3985,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(1239,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__greatest) ).
thf(5928,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(858,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bijI) ).
thf(4503,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ D ) @ B ) ) @ c_FunDef_Opair__less ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ c_FunDef_Omin__strict ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ A ) ) ) @ c_FunDef_Omin__strict ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__insertI) ).
thf(2524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ D ) @ B ) ) @ c_FunDef_Opair__less ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ c_FunDef_Omin__strict ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ A ) ) ) @ c_FunDef_Omin__strict ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(300,axiom,
c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pair__less) ).
thf(2376,plain,
c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__le) ).
thf(3536,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(601,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(3547,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ A )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Int) ).
thf(3070,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ A )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Ounion__idem) ).
thf(2970,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ C ) @ ( tc_prod @ C @ D ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( c_COMBC @ C @ D @ ( tc_prod @ C @ D ) ) @ ( c_Product__Type_OPair @ C @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ D ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__product) ).
thf(1916,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ C ) @ ( tc_prod @ C @ D ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( c_COMBC @ C @ D @ ( tc_prod @ C @ D ) ) @ ( c_Product__Type_OPair @ C @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ D ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(587,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(3504,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Compl) ).
thf(2849,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(459,axiom,
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).
thf(2981,plain,
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
thf(5097,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(1175,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterI) ).
thf(5698,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).
thf(3372,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
thf(2048,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__subset) ).
thf(2859,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(1784,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(855,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__Int) ).
thf(4494,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(3811,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(1080,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
thf(5395,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(524,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
thf(3240,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ D @ C @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ D @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).
thf(2393,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ D @ C @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ D @ C ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Int) ).
thf(3086,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
= ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
thf(1652,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
= ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(3081,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(659,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(3758,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Ovimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UNIV) ).
thf(3283,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Ovimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(385,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
<=> ~ ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ ( hAPP @ C @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ C @ D ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).
thf(2674,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Owf @ B @ A )
=> ~ ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ ( hAPP @ C @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ C @ D ) ) ) @ A ) ) )
& ( ~ ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ ( hAPP @ C @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ C @ D ) ) ) @ A ) )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(2016,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(1388,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ C @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__image__eq) ).
thf(3272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ C @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__INT) ).
thf(4801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(992,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffI) ).
thf(5050,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(1225,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
thf(5876,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ G @ F ) @ B @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ G @ F @ B ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__imageI) ).
thf(3604,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ G @ F ) @ B @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ G @ F @ B ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
thf(4381,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectI) ).
thf(1520,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(688,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) ) @ A ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__INFI__fold__inf) ).
thf(3868,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) ) @ A ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__conv) ).
thf(4758,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(1115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(5503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(967,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
thf(4946,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(392,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__singleton) ).
thf(2695,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ ( hAPP @ ( c_COMBK @ E @ F ) @ C ) ) @ B ) @ A )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_K__record__comp) ).
thf(1488,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ ( hAPP @ ( c_COMBK @ E @ F ) @ C ) ) @ B ) @ A )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(2161,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(4096,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(1140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD1) ).
thf(5595,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(759,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Pow__subset) ).
thf(4149,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__empty) ).
thf(4413,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(918,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I2_J) ).
thf(4764,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(1037,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__iff) ).
thf(5207,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1177,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(5703,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) )
=> ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
thf(4273,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(1255,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ D @ E ) @ B ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).
thf(5997,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ D @ E ) @ B ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Un) ).
thf(3568,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__def) ).
thf(5432,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(1261,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ v_G ) @ ( hAPP @ ( c_Set_Oimage @ tc_Com_Opname @ t_a @ v_mgt__call ) @ v_U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(6016,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ v_G ) @ ( hAPP @ ( c_Set_Oimage @ tc_Com_Opname @ t_a @ v_mgt__call ) @ v_U ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(867,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
thf(4537,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(668,axiom,
! [A: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__remove) ).
thf(3796,plain,
! [A: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__Int) ).
thf(3023,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(989,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
thf(5039,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectD) ).
thf(1669,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__insert__iff) ).
thf(3118,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
thf(5033,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(711,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= A ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I1_J) ).
thf(3964,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= A ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1071,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ C ) @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2I) ).
thf(5363,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ C ) @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetI) ).
thf(3051,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(5471,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ A ) ) ) @ c_FunDef_Opair__less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI2) ).
thf(4796,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ A ) ) ) @ c_FunDef_Opair__less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(5011,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
thf(2308,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(937,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ C ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ D ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ D ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).
thf(4837,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ C ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ D ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ D ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__f__f) ).
thf(3695,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion__inter) ).
thf(4099,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ F @ E @ D @ C @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).
thf(2738,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ F @ E @ D @ C @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ C ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ A ) ) )
=> ~ ! [E: $i] :
( ( C
= ( hAPP @ ( c_Relation_OImage @ D @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientE) ).
thf(1635,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ A ) ) )
=> ~ ! [E: $i] :
( ( C
= ( hAPP @ ( c_Relation_OImage @ D @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD2) ).
thf(4822,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( c_Relation_OImage @ D @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__eq__UN) ).
thf(3594,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( c_Relation_OImage @ D @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Omax__extp @ D @ C @ B @ A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Osimps) ).
thf(4573,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Omax__extp @ D @ C @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(5086,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
thf(1997,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectE) ).
thf(2166,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I5_J) ).
thf(5539,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(943,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C )
= B )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(4854,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C )
= B )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ B ) @ A ) )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).
thf(1897,plain,
! [A: $i,B: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ B ) @ A ) )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(648,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Inter) ).
thf(3719,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(1133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(5578,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) )
=> ( ( c_Transitive__Closure_Ortrancl @ C @ A )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
thf(2311,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) )
=> ( ( c_Transitive__Closure_Ortrancl @ C @ A )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(343,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
thf(2521,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).
thf(2119,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ E ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__eq) ).
thf(2478,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ E ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ B ) ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__le__iff) ).
thf(2624,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ B ) ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ D ) @ A ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).
thf(1806,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__disjoint) ).
thf(3779,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(452,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc) ).
thf(2955,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(994,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(5054,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(761,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) ) @ A ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__SUPR__fold__sup) ).
thf(4154,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) ) @ A ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(506,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).
thf(3160,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(2065,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(386,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
thf(2679,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).
thf(4704,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib) ).
thf(4228,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
thf(2538,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).
thf(1408,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientI) ).
thf(2642,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un) ).
thf(3815,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
<=> ( ( hAPP @ B @ D )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__singleton__eq) ).
thf(3764,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ B @ D )
= A ) )
& ( ( ( hAPP @ B @ D )
= A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ E ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ E ) @ A ) ) ) )
=> ( ( D = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
thf(2415,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ E ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ E ) @ A ) ) ) )
=> ( ( D = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I10_J) ).
thf(5520,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OPow @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__def) ).
thf(1894,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OPow @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(2493,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__apply) ).
thf(1524,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(933,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionI) ).
thf(4828,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert__remove) ).
thf(3515,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(898,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).
thf(4699,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(1152,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
thf(5631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(1057,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Set_Oimage @ D @ E @ C ) ) @ ( hAPP @ ( c_Set_OPow @ D ) @ B ) ) ) @ ( hAPP @ ( c_Set_OPow @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__mono) ).
thf(5303,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Set_Oimage @ D @ E @ C ) ) @ ( hAPP @ ( c_Set_OPow @ D ) @ B ) ) ) @ ( hAPP @ ( c_Set_OPow @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(1211,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ B @ ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ A ) @ C ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__surj) ).
thf(5827,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ B @ ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ A ) @ C ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(1218,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).
thf(5853,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OField @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Un) ).
thf(2284,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OField @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(273,axiom,
( c_FunDef_Omax__strict
= ( c_Wellfounded_Omax__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__strict__def) ).
thf(2257,plain,
( c_FunDef_Omax__strict
= ( c_Wellfounded_Omax__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(1589,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1233,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__lower) ).
thf(5901,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(1227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).
thf(5880,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ A ) @ D ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).
thf(3710,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ A ) @ D ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ A ) @ D ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(969,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Union) ).
thf(4958,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I3_J) ).
thf(2945,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ C @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__empty) ).
thf(2856,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ C @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__f) ).
thf(4176,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(1146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(5616,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty2) ).
thf(1439,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(775,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__additive) ).
thf(4203,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(1160,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__diff__subset) ).
thf(5657,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(869,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
thf(4541,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(1232,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ B @ F ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__subset__iff) ).
thf(5894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ B @ F ) ) @ A ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(1254,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep) ).
thf(5994,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(409,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(2780,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__sym) ).
thf(1821,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(161,axiom,
! [A: $i] : ( c_Wellfounded_Owf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Wellfounded_Ofinite__psubset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__finite__psubset) ).
thf(1862,plain,
! [A: $i] : ( c_Wellfounded_Owf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Wellfounded_Ofinite__psubset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(3006,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD1) ).
thf(2252,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(2553,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(2461,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(895,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__set__diff) ).
thf(4684,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(1198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ A @ F ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ F ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset__induct) ).
thf(5780,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ A @ F ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ F ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert) ).
thf(4635,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1073,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ! [G: $i,H: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ G ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ B @ G ) @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitE) ).
thf(5367,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ! [G: $i,H: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ G ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ B @ G ) @ H ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1258,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
<=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__iff) ).
thf(6004,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) )
& ( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(75,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(1557,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(4009,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int1) ).
thf(2314,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(935,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
thf(4833,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(737,axiom,
! [A: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__empty) ).
thf(4064,plain,
! [A: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(1630,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(701,axiom,
! [A: $i] : ( c_Fun_Obij__betw @ A @ A @ ( c_Fun_Oid @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__id) ).
thf(3932,plain,
! [A: $i] : ( c_Fun_Obij__betw @ A @ A @ ( c_Fun_Oid @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(977,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
thf(4985,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(842,axiom,
! [A: $i] :
( ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
thf(4452,plain,
! [A: $i] :
( ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__eq__Union) ).
thf(4277,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__Suc0__iff) ).
thf(2757,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
thf(3034,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(1079,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D2) ).
thf(5392,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(1838,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1059,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ G @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD_H) ).
thf(5318,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ G @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(1281,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ F @ B ) @ A ) )
= ( hAPP @ ( c_Set_Oimage @ C @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ C ) @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image) ).
thf(6080,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ F @ B ) @ A ) )
= ( hAPP @ ( c_Set_Oimage @ C @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ C ) @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) )
=> ( ! [I: $i,J: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ! [K: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
thf(2289,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) )
=> ( ! [I: $i,J: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ! [K: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Ofun__upd @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ C @ B ) @ C @ A )
= ( c_Fun_Ofun__upd @ F @ E @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
thf(2647,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Ofun__upd @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ C @ B ) @ C @ A )
= ( c_Fun_Ofun__upd @ F @ E @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(579,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(3480,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(154,axiom,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ c_FunDef_Omin__strict ) @ c_FunDef_Omin__weak ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__rpair__set) ).
thf(1841,plain,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ c_FunDef_Omin__strict ) @ c_FunDef_Omin__weak ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1240,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) )
= ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).
thf(5931,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) )
= ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) )
=> ~ ( c_Fun_Oinj__on @ C @ D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
thf(3627,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) )
=> ~ ( c_Fun_Oinj__on @ C @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Oinj__on @ H @ G @ F @ E )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ I ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ ( hAPP @ B @ I ) ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ H @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ H @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ D ) @ ( c_Set_Oimage @ H @ G @ F ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__INT) ).
thf(5216,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Oinj__on @ H @ G @ F @ E )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ I ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ ( hAPP @ B @ I ) ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ H @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ H @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ D ) @ ( c_Set_Oimage @ H @ G @ F ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(226,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
thf(2086,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert) ).
thf(5646,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(638,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert__remove) ).
thf(3674,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(1182,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplE) ).
thf(5725,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(2535,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(1364,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(1496,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(549,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint) ).
thf(3348,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1266,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( c_FunDef_Oreduction__pair @ B @ ( hAPP @ ( hAPP @ ( c_FunDef_Orp__inv__image @ D @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(6029,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( c_FunDef_Oreduction__pair @ B @ ( hAPP @ ( hAPP @ ( c_FunDef_Orp__inv__image @ D @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__eq__Union__image) ).
thf(2867,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).
thf(2418,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(963,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
thf(4933,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ C @ C @ A @ B )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
thf(5742,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ C @ C @ A @ B )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(453,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(2962,plain,
class_Orderings_Oord @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1197,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__iff) ).
thf(5775,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(1004,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ H ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__I) ).
thf(5094,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ H ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(567,axiom,
! [A: $i] :
( ( hAPP @ ( c_Set_OPow @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__UNIV) ).
thf(3423,plain,
! [A: $i] :
( ( hAPP @ ( c_Set_OPow @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).
thf(2481,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(2592,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__SigmaI) ).
thf(2244,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int) ).
thf(3512,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(856,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).
thf(4497,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq2) ).
thf(4067,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1062,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ D @ B ) @ A ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__subset) ).
thf(5326,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ D @ B ) @ A ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(950,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
thf(4890,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(691,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion) ).
thf(3876,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ? [C: $i] : ( c_Fun_Obij__betw @ B @ tc_Nat_Onat @ C @ A @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__bij__betw__finite__nat) ).
thf(2693,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ? [C: $i] : ( c_Fun_Obij__betw @ B @ tc_Nat_Onat @ C @ A @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ ( tc_prod @ B @ A ) ) @ ( c_Product__Type_OPair @ B @ A ) )
= ( c_Fun_Oid @ ( tc_prod @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__Pair) ).
thf(4209,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ ( tc_prod @ B @ A ) ) @ ( c_Product__Type_OPair @ B @ A ) )
= ( c_Fun_Oid @ ( tc_prod @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__eq) ).
thf(4481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Inf__fold__inf) ).
thf(2506,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
<=> ? [D: $i,E: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
& ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ E )
= A )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__eq) ).
thf(3380,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ? [D: $i,E: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
& ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ E )
= A )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
& ( ? [D: $i,E: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
& ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ E )
= A )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B )
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).
thf(1562,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).
thf(4084,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1282,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( c_Set_Oimage @ F @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__compose) ).
thf(6083,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( c_Set_Oimage @ F @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(1091,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(5435,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(5688,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(822,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).
thf(4394,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(1122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
thf(5528,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(173,axiom,
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__0) ).
thf(1905,plain,
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ F @ E @ D @ C @ B @ A )
=> ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oempty) ).
thf(3981,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ F @ E @ D @ C @ B @ A )
=> ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I3_J) ).
thf(3146,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__subsets) ).
thf(1509,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(699,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ D @ A ) @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) ) ) @ C )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__inv__o__cancel) ).
thf(3921,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ D @ A ) @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) ) ) @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__right) ).
thf(2846,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(1958,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1158,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD2) ).
thf(5652,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ F @ E @ D @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).
thf(3571,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ F @ E @ D @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(826,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
thf(4405,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition2) ).
thf(2914,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).
thf(3031,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(2107,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1229,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).
thf(5886,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(844,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__insert) ).
thf(4458,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
<=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__def) ).
thf(3576,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A ) ) )
& ( ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A ) )
=> ( c_Fun_Obij__betw @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
thf(2318,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter) ).
thf(3206,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(1191,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__anti__mono) ).
thf(5757,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__SucD) ).
thf(2037,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__conv) ).
thf(2927,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( c_Set_Ovimage @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Union) ).
thf(3975,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( c_Set_Ovimage @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(1990,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(944,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
thf(4859,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__commute) ).
thf(2684,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(538,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(3292,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(437,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_Fun_Oid @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id) ).
thf(2899,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_Fun_Oid @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
thf(5358,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(1015,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__mono) ).
thf(5133,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__D) ).
thf(4812,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(73,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(1551,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib) ).
thf(2942,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(6069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).
thf(1961,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( c_Equiv__Relations_Oquotient @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ C ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__diff1) ).
thf(3913,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( c_Equiv__Relations_Oquotient @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ C ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(497,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__Suc) ).
thf(3112,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(2661,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(1108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ C ) )
=> ( ( hAPP @ B @ I )
= ( hAPP @ A @ I ) ) )
=> ( ( hAPP @ ( hAPP @ D @ B ) @ C )
= ( hAPP @ ( hAPP @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Ocong) ).
thf(5484,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ C ) )
=> ( ( hAPP @ B @ I )
= ( hAPP @ A @ I ) ) )
=> ( ( hAPP @ ( hAPP @ D @ B ) @ C )
= ( hAPP @ ( hAPP @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(1139,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).
thf(5592,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnI) ).
thf(5523,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert2) ).
thf(3209,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(1094,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
<=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__iff) ).
thf(5446,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) )
& ( ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).
thf(3988,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(2513,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(1845,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(913,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__singleton) ).
thf(4749,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(1095,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) @ B ) )
=> ( c_Wellfounded_OwfP @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__subset) ).
thf(5452,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) @ B ) )
=> ( c_Wellfounded_OwfP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(991,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(5047,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(1179,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryD) ).
thf(5716,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__insert) ).
thf(3737,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ F @ C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__ImageI) ).
thf(1770,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ F @ C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).
thf(4360,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(1117,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Fun_Oid @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__apply) ).
thf(5514,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Fun_Oid @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).
thf(3507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1142,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Un) ).
thf(5602,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(1010,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__I) ).
thf(5111,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(1077,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__empty) ).
thf(5388,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) )
=> ( c_Fun_Oinj__on @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).
thf(2060,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) )
=> ( c_Fun_Oinj__on @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(964,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Fun_Oid @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__def) ).
thf(4939,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Fun_Oid @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
thf(1400,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1081,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(5399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(2192,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(891,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ E @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__the__inv__into) ).
thf(4673,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ E @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(1113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
thf(5499,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(529,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(3260,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).
thf(2588,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert__distrib) ).
thf(4922,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downward) ).
thf(1647,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).
thf(3228,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(886,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff2__less) ).
thf(4641,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(970,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__upper) ).
thf(4961,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(2386,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(1000,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
thf(5079,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Ovimage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__empty) ).
thf(4324,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Ovimage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ E @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff1__fold__graph) ).
thf(4630,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ E @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__binary) ).
thf(1499,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(628,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ c_Int_ORep__Integ @ A ) ) @ c_Int_OInteg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ) ).
thf(3642,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ c_Int_ORep__Integ @ A ) ) @ c_Int_OInteg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(955,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
thf(4905,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ B ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ B ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__distrib) ).
thf(1300,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ B ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ B ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(2920,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(1270,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Opos__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Opos__single @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__single__def) ).
thf(6037,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Opos__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Opos__single @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I7_J) ).
thf(3722,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(5912,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(780,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(4222,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__subset) ).
thf(3026,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Un) ).
thf(3655,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ C @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__image__eq) ).
thf(3544,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ C @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(1021,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
thf(5152,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(786,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ tc_HOL_Obool @ C ) @ A ) @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__image__Collect__eq) ).
thf(4241,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ tc_HOL_Obool @ C ) @ A ) @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ E @ F @ D ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__INT__subset) ).
thf(2044,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ E @ F @ D ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(1579,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(647,axiom,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(3715,plain,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__lower) ).
thf(2569,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(836,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib) ).
thf(4437,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ A ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oeq__fold) ).
thf(1790,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ A ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1269,axiom,
hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Com_Opname ) @ v_U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(6036,plain,
hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Com_Opname ) @ v_U ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(770,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(4190,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(675,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Pow__Union) ).
thf(3818,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
<=> ? [E: $i] :
( ( A
= ( hAPP @ B @ E ) )
& ! [F: $i] :
( ( A
= ( hAPP @ B @ F ) )
=> ( F = E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
thf(3885,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ? [E: $i] :
( ( A
= ( hAPP @ B @ E ) )
& ! [F: $i] :
( ( A
= ( hAPP @ B @ F ) )
=> ( F = E ) ) ) )
& ( ? [E: $i] :
( ( A
= ( hAPP @ B @ E ) )
& ! [F: $i] :
( ( A
= ( hAPP @ B @ F ) )
=> ( F = E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(677,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__eq) ).
thf(3823,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
<=> ! [C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ E ) @ D ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
thf(2337,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Owf @ B @ A )
=> ! [C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ E ) @ D ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ C ) ) ) ) ) )
& ( ! [C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ E ) @ D ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ C ) ) ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(987,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).
thf(5030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ D @ C @ B )
=> ( ( hAPP @ ( c_Fun_Ocomp @ C @ C @ C @ ( hAPP @ B @ A ) ) @ ( hAPP @ B @ A ) )
= ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).
thf(2128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ D @ C @ B )
=> ( ( hAPP @ ( c_Fun_Ocomp @ C @ C @ C @ ( hAPP @ B @ A ) ) @ ( hAPP @ B @ A ) )
= ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1022,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OemptyI) ).
thf(5154,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1035,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
thf(5203,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(623,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oremove) ).
thf(3623,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(563,axiom,
! [A: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__UNIV) ).
thf(3412,plain,
! [A: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
thf(2247,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ B @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) ) @ ( c_Orderings_Otop__class_Otop @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fold__inf) ).
thf(1934,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ B @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) ) @ ( c_Orderings_Otop__class_Otop @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__disjoint) ).
thf(3488,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(495,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(3107,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).
thf(5675,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(1702,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(757,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(4143,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(1170,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
thf(5685,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(808,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(4342,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Int) ).
thf(2939,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(710,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Oinj__on @ G @ F @ E @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) )
=> ( ( c_Fun_Oinj__on @ D @ G @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) ) ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ D @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ D @ E ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ G @ D @ F @ ( c_Fun_Othe__inv__into @ D @ G @ B @ C ) ) @ ( c_Fun_Othe__inv__into @ G @ F @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) @ E ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__comp) ).
thf(3961,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Oinj__on @ G @ F @ E @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) )
=> ( ( c_Fun_Oinj__on @ D @ G @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) ) ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ D @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ D @ E ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ G @ D @ F @ ( c_Fun_Othe__inv__into @ D @ G @ B @ C ) ) @ ( c_Fun_Othe__inv__into @ G @ F @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) @ E ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(791,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
thf(4257,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ C @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__def) ).
thf(1849,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ C @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__same__card) ).
thf(3652,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(564,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__left) ).
thf(3415,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1279,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hAPP @ C @ ( hAPP @ D @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(6073,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hAPP @ C @ ( hAPP @ D @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(1151,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(5628,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
thf(4133,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(463,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(2992,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I9_J) ).
thf(4624,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__disjoint) ).
thf(4611,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Ofinite__psubset @ C ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
thf(3356,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Ofinite__psubset @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Ofinite__psubset @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(1145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).
thf(5613,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(1043,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
<=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
thf(5240,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) )
& ( ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(294,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(2357,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__disjoint) ).
thf(2843,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(52,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
thf(1485,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ D @ B ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__const) ).
thf(2711,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ D @ B ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__quotient) ).
thf(1504,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).
thf(4431,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(784,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).
thf(4235,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1283,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_New__Random__Sequence_Opos__union @ F @ E @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__union @ F @ ( hAPP @ ( hAPP @ ( hAPP @ E @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__union__def) ).
thf(6086,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_New__Random__Sequence_Opos__union @ F @ E @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__union @ F @ ( hAPP @ ( hAPP @ ( hAPP @ E @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OField @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OField @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__insert) ).
thf(4093,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OField @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OField @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(2722,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
thf(2807,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(1006,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnE) ).
thf(5100,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD2) ).
thf(2458,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
thf(1649,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff1) ).
thf(4851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__distrib) ).
thf(3067,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).
thf(2870,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(1124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I10_J) ).
thf(5536,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__eq__Inter__image) ).
thf(3533,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OemptyI) ).
thf(3874,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ A ) ) ) @ c_FunDef_Opair__less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI1) ).
thf(2347,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ A ) ) ) @ c_FunDef_Opair__less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(650,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq) ).
thf(3725,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
thf(1734,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1195,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
thf(5771,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).
thf(3168,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ A @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__mono) ).
thf(1940,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ A @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).
thf(1421,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(560,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
<=> ? [C: $i,D: $i] :
( A
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ B @ D ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__conv__nat__seg__image) ).
thf(3400,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ? [C: $i,D: $i] :
( A
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ B @ D ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ C ) ) ) ) )
& ( ? [C: $i,D: $i] :
( A
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ B @ D ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(612,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(3584,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__eq) ).
thf(4651,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
thf(5490,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__empty2) ).
thf(3565,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__subset) ).
thf(2088,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(1188,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( v_P @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
thf(5749,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( v_P @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(48,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
thf(1459,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(490,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(3092,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(114,axiom,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Wellfounded_Omeasure @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measure) ).
thf(1685,plain,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Wellfounded_Omeasure @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_OwfP @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ B @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( c_member @ ( tc_prod @ B @ B ) ) ) ) @ ( c_Product__Type_OPair @ B @ B ) ) ) ) @ A ) )
<=> ( c_Wellfounded_Owf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__wf__eq) ).
thf(2885,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_OwfP @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ B @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( c_member @ ( tc_prod @ B @ B ) ) ) ) @ ( c_Product__Type_OPair @ B @ B ) ) ) ) @ A ) )
=> ( c_Wellfounded_Owf @ B @ A ) )
& ( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_OwfP @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ B @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( c_member @ ( tc_prod @ B @ B ) ) ) ) @ ( c_Product__Type_OPair @ B @ B ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ F ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(4944,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ F ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(889,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
thf(4656,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ D ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__fold__sup) ).
thf(3188,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ D ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1116,axiom,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A )
= ( hAPP @ ( c_Set_OPow @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cantors__paradox) ).
thf(5510,plain,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A )
= ( hAPP @ ( c_Set_OPow @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV1) ).
thf(2215,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1241,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).
thf(5934,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(1517,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__setsum) ).
thf(2490,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(747,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__if) ).
thf(4102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(543,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__transfer) ).
thf(3320,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Times__UNIV) ).
thf(2305,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(1013,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ F ) @ A ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I1) ).
thf(5124,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ F ) @ A ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ D @ B )
!= ( hAPP @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
thf(4170,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ D @ B )
!= ( hAPP @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1,conjecture,
( v_G
= ( hAPP @ ( c_Set_Oimage @ tc_Com_Opname @ t_a @ v_mgt__call ) @ v_U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(2,negated_conjecture,
( v_G
!= ( hAPP @ ( c_Set_Oimage @ tc_Com_Opname @ t_a @ v_mgt__call ) @ v_U ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1289,plain,
( v_G
!= ( hAPP @ ( c_Set_Oimage @ tc_Com_Opname @ t_a @ v_mgt__call ) @ v_U ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__wfD) ).
thf(1453,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1220,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI1) ).
thf(5860,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(1064,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ? [E: $i] :
( ( c_Fun_Oinj__on @ D @ B @ E @ C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ E ) @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
thf(5332,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( ? [E: $i] :
( ( c_Fun_Oinj__on @ D @ B @ E @ C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ E ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) )
=> ? [E: $i] :
( ( c_Fun_Oinj__on @ D @ B @ E @ C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ E ) @ C ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(2658,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
thf(2775,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(906,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oremove) ).
thf(4730,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(893,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ ( c_Product__Type_Ocurry @ D @ C @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__curry) ).
thf(4678,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ ( c_Product__Type_Ocurry @ D @ C @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(956,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Int) ).
thf(4913,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(1280,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__single @ C @ B ) @ A )
= ( hAPP @ ( c_Lazy__Sequence_Osingle @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
thf(6077,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__single @ C @ B ) @ A )
= ( hAPP @ ( c_Lazy__Sequence_Osingle @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(789,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ E ) @ ( hAPP @ ( c_Set_Ovimage @ A @ C @ F ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageI) ).
thf(4250,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ E ) @ ( hAPP @ ( c_Set_Ovimage @ A @ C @ F ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(546,axiom,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBI @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__def) ).
thf(3336,plain,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBI @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
thf(3003,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Finite__Set_Ofolding @ K @ J @ I @ H )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ G @ E @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ C @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ C @ D ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).
thf(3368,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Finite__Set_Ofolding @ K @ J @ I @ H )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ G @ E @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ C @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ C @ D ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).
thf(4710,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( c_Fun_Oinj__on @ E @ B @ A @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ F @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on) ).
thf(3864,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( c_Fun_Oinj__on @ E @ B @ A @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ F @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
thf(1385,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(110,axiom,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oempty) ).
thf(1674,plain,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(427,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(2855,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__subset) ).
thf(1639,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(982,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).
thf(5008,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__empty2) ).
thf(2406,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(894,axiom,
! [A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__UNIV) ).
thf(4681,plain,
! [A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).
thf(5191,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(1202,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ H @ B ) @ A ) ) @ E ) )
=> ( ( c_Fun_Obij__betw @ C @ H @ B @ A @ E )
<=> ( c_Fun_Obij__betw @ C @ G @ ( hAPP @ ( c_Fun_Ocomp @ H @ G @ C @ F ) @ B ) @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__comp__iff2) ).
thf(5800,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ H @ B ) @ A ) ) @ E ) )
=> ( ( ( c_Fun_Obij__betw @ C @ H @ B @ A @ E )
=> ( c_Fun_Obij__betw @ C @ G @ ( hAPP @ ( c_Fun_Ocomp @ H @ G @ C @ F ) @ B ) @ A @ D ) )
& ( ( c_Fun_Obij__betw @ C @ G @ ( hAPP @ ( c_Fun_Ocomp @ H @ G @ C @ F ) @ B ) @ A @ D )
=> ( c_Fun_Obij__betw @ C @ H @ B @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ C ) ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Inter__image) ).
thf(4126,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ C ) ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ ( tc_prod @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ D @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ F ) @ ( c_Product__Type_OPair @ E @ D ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( c_Set_Oimage @ F @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ E ) @ ( c_Set_Ovimage @ F @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ E ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__split__eq__Sigma) ).
thf(2823,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ ( tc_prod @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ D @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ F ) @ ( c_Product__Type_OPair @ E @ D ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( c_Set_Oimage @ F @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ E ) @ ( c_Set_Ovimage @ F @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ E ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).
thf(4715,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimage__iff) ).
thf(3104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(718,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
thf(3991,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(1264,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_New__DSequence_Opos__map @ E @ D @ C @ B @ A )
= ( c_Lazy__Sequence_Omap @ E @ D @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__map__def) ).
thf(6023,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_New__DSequence_Opos__map @ E @ D @ C @ B @ A )
= ( c_Lazy__Sequence_Omap @ E @ D @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(1207,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__E) ).
thf(5813,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(1041,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
thf(5228,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
thf(2026,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__quotient) ).
thf(2526,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(864,axiom,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBI @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__def) ).
thf(4527,plain,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBI @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(953,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(4900,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
thf(2152,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(714,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Osingleton) ).
thf(3978,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(410,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(2796,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hAPP @ D @ I )
= E ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).
thf(3879,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hAPP @ D @ I )
= E ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntE) ).
thf(5692,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(1213,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__o) ).
thf(5837,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
thf(2362,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B )
= A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(1607,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union2) ).
thf(3552,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1065,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert) ).
thf(5336,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(1222,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ G ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__I) ).
thf(5864,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ G ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(1246,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ C @ A @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(5963,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ C @ A @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(1491,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ C @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ C @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ A ) ) @ D )
= ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__image) ).
thf(3181,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ C @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ C @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ A ) ) @ D )
= ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__asym) ).
thf(2384,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(329,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(2475,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ A ) @ B ) ) @ C ) )
=> ? [G: $i] : ( c_Fun_Obij__betw @ F @ E @ G @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cantor__Bernstein) ).
thf(2912,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ A ) @ B ) ) @ C ) )
=> ? [G: $i] : ( c_Fun_Obij__betw @ F @ E @ G @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(805,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
thf(4321,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ B )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oremove) ).
thf(3267,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ B )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff) ).
thf(5109,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(998,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).
thf(5072,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(550,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(3351,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(1224,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__subset__iff) ).
thf(5869,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ A @ F ) ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(719,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
<=> ( ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__insert) ).
thf(3993,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) )
& ( ( ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__mono) ).
thf(5590,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(230,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(2095,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(740,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(4074,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ A ) @ B ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ F ) @ C )
= ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
thf(5517,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ A ) @ B ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ F ) @ C )
= ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(2294,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
& ( ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1165,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(5672,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).
thf(1444,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(1442,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oeq__fold) ).
thf(2917,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(815,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(4372,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(660,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ A ) ) @ c_FunDef_Omax__strict ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__emptyI) ).
thf(3761,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ A ) ) @ c_FunDef_Omax__strict ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(278,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(2287,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
thf(2102,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Set_Oinsert @ C ) ) @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__UN) ).
thf(3785,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Set_Oinsert @ C ) ) @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(71,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__less__nat) ).
thf(1546,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).
thf(1625,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(531,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ G @ D @ A @ F @ C )
=> ( ( c_Fun_Obij__betw @ G @ D @ A @ E @ B )
=> ( c_Fun_Obij__betw @ G @ D @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__Disj__Un) ).
thf(3264,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ G @ D @ A @ F @ C )
=> ( ( c_Fun_Obij__betw @ G @ D @ A @ E @ B )
=> ( c_Fun_Obij__betw @ G @ D @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold_H) ).
thf(3521,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(1527,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(949,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
thf(4885,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
thf(4367,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ E @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__imp__inj__on) ).
thf(3469,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ E @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__def) ).
thf(3658,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).
thf(2930,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(262,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(2218,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(748,axiom,
! [A: $i,B: $i,C: $i] : ( c_Fun_Oinj__on @ ( tc_prod @ C @ B ) @ ( tc_prod @ B @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ ( tc_prod @ B @ C ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ ( tc_prod @ B @ C ) ) @ ( c_Product__Type_OPair @ B @ C ) ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__inj__on) ).
thf(4114,plain,
! [A: $i,B: $i,C: $i] : ( c_Fun_Oinj__on @ ( tc_prod @ C @ B ) @ ( tc_prod @ B @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ ( tc_prod @ B @ C ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ ( tc_prod @ B @ C ) ) @ ( c_Product__Type_OPair @ B @ C ) ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib2) ).
thf(4399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( D != E )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__partition) ).
thf(4687,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( D != E )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(2155,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(817,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Diff__eq) ).
thf(4378,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).
thf(4809,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I7_J) ).
thf(2983,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(398,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
thf(2719,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__partition) ).
thf(4254,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__empty1) ).
thf(3733,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Product__Type_Ocurry @ D @ C @ B @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__split) ).
thf(3601,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Product__Type_Ocurry @ D @ C @ B @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(2233,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(904,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(4719,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(1273,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(6050,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(1089,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Fun_Oinj__on @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
thf(5430,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Fun_Oinj__on @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hAPP @ c_Nat_OSuc @ B )
!= A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(3837,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hAPP @ c_Nat_OSuc @ B )
!= A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Wellfounded_Omlex__prod @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__mlex) ).
thf(2604,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Wellfounded_Omlex__prod @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( c_Fun_Oinj__on @ D @ B @ A @ C )
<=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
thf(4841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( ( c_Fun_Oinj__on @ D @ B @ A @ C )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) )
& ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ D @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ B @ F ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect__mono) ).
thf(1986,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ B @ F ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ tc_HOL_Obool @ D ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
thf(2008,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ tc_HOL_Obool @ D ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__Un__disjoint) ).
thf(1303,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1105,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
thf(5477,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(1074,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__E) ).
thf(5371,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__refl) ).
thf(2050,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(812,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Diff) ).
thf(4357,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(854,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__Int) ).
thf(4491,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(1757,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I7_J) ).
thf(3203,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(843,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageD) ).
thf(4455,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__set__diff) ).
thf(3309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__flatten) ).
thf(3015,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(727,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) @ A )
=> ( c_Fun_Oinj__on @ F @ D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI2) ).
thf(4029,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) @ A )
=> ( c_Fun_Oinj__on @ F @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__mult @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ B @ G ) ) ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ D ) )
=> ( ( G != H )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ B @ H ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ E @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ F ) ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__UN__disjoint) ).
thf(1314,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__mult @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ B @ G ) ) ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ D ) )
=> ( ( G != H )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ B @ H ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ E @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ F ) ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1099,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__D) ).
thf(5462,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ F ) )
& ( D
= ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset__image) ).
thf(5441,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ F ) )
& ( D
= ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1066,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Pow__iff) ).
thf(5339,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(1271,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(6040,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__subset) ).
thf(2668,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(90,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
thf(1610,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int2) ).
thf(3805,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(39,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(1436,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(758,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__UNIV) ).
thf(4146,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_OImage @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Image) ).
thf(2751,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_OImage @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(411,axiom,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ c_FunDef_Omax__strict ) @ c_FunDef_Omax__weak ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__rpair__set) ).
thf(2800,plain,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ c_FunDef_Omax__strict ) @ c_FunDef_Omax__weak ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(694,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I1_J) ).
thf(3897,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(733,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_OPow @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_Set_OPow @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__INT__eq) ).
thf(4051,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_OPow @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_Set_OPow @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(915,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__left) ).
thf(4755,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__single__insert) ).
thf(3560,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(951,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff2) ).
thf(4895,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(2186,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(3558,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(1253,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).
thf(5990,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( c_Fun_Obij__betw @ G @ C @ B @ D @ A )
=> ( c_Fun_Obij__betw @ H @ C @ ( hAPP @ ( c_Fun_Ocomp @ G @ C @ H @ B ) @ F ) @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__trans) ).
thf(4007,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( c_Fun_Obij__betw @ G @ C @ B @ D @ A )
=> ( c_Fun_Obij__betw @ H @ C @ ( hAPP @ ( c_Fun_Ocomp @ G @ C @ H @ B ) @ F ) @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(1008,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
thf(5105,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union) ).
thf(4157,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ G @ H @ H ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ H @ ( tc_fun @ H @ H ) @ G ) @ F ) @ B ) ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ ( hAPP @ D @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Odistrib) ).
thf(1693,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ G @ H @ H ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ H @ ( tc_fun @ H @ H ) @ G ) @ F ) @ B ) ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ ( hAPP @ D @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(2070,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(1136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitI) ).
thf(5586,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(544,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(3323,plain,
! [A: $i,B: $i] :
( ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
thf(2714,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(568,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert) ).
thf(3426,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__empty) ).
thf(1891,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(946,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
thf(4865,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(838,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(4442,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).
thf(4034,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I3_J) ).
thf(3843,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(1034,axiom,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__empty) ).
thf(5200,plain,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).
thf(4318,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( c_Fun_Ofun__upd @ B @ A @ E @ D @ C )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(1742,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( c_Fun_Ofun__upd @ B @ A @ E @ D @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1203,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).
thf(5803,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(2430,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
thf(1532,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1204,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowI) ).
thf(5806,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1017,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
thf(5140,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).
thf(2265,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1134,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowD) ).
thf(5581,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(851,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(4484,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(1149,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__INT) ).
thf(5623,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(809,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
thf(4345,plain,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1103,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
thf(5473,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(1067,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
thf(5344,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib1) ).
thf(2241,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(1244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
<=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__Un) ).
thf(5945,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) )
& ( ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
thf(4848,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(553,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(3362,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
thf(2810,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(752,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_COMBI @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).
thf(4129,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_COMBI @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
thf(1829,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(995,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__subset__Compl__iff) ).
thf(5061,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ G @ B ) @ F @ A )
= ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ F @ A ) @ G @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
thf(1976,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ G @ B ) @ F @ A )
= ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ F @ A ) @ G @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1250,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
thf(5975,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(17,axiom,
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__greaterThan__UNIV) ).
thf(1357,plain,
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(859,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Compl__self__eq) ).
thf(4506,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(358,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(2583,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(1168,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__into) ).
thf(5681,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(4410,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
thf(4659,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__imp__bij__inv) ).
thf(3538,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(1101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( C != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
thf(5468,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( C != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(704,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) @ c_FunDef_Omin__weak ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmin__emptyI) ).
thf(3939,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) @ c_FunDef_Omin__weak ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(1231,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2E) ).
thf(5891,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(1069,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( F
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ A @ G ) @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI2) ).
thf(5354,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( F
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ A @ G ) @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(389,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(2687,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I6_J) ).
thf(2864,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(654,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__comp) ).
thf(3740,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Diff__distrib1) ).
thf(1880,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ D @ ( tc_fun @ A @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ A @ C ) @ D ) @ ( c_COMBK @ C @ A ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).
thf(1431,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ D @ ( tc_fun @ A @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ A @ C ) @ D ) @ ( c_COMBK @ C @ A ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__insert) ).
thf(2484,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastLessThan) ).
thf(1885,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ D @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold__graphE) ).
thf(3494,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ D @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
thf(3753,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product__singleton) ).
thf(2754,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
thf(4627,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(222,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(2074,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_Nat_Onat @ D ) @ ( c_Finite__Set_Ocard @ B ) ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__SigmaI) ).
thf(2832,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_Nat_Onat @ D ) @ ( c_Finite__Set_Ocard @ B ) ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right) ).
thf(5569,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(735,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Ovimage @ B @ B @ ( c_Fun_Oid @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__id) ).
thf(4056,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Ovimage @ B @ B @ ( c_Fun_Oid @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
thf(5293,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
thf(2470,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(637,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ G ) @ F ) ) @ A ) )
=> ( G = F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
thf(3669,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ G ) @ F ) ) @ A ) )
=> ( G = F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
thf(1331,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(577,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I8_J) ).
thf(3474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ E @ D @ C )
=> ( c_Finite__Set_Ofun__left__comm__idem @ B @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ D ) @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).
thf(2672,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ E @ D @ C )
=> ( c_Finite__Set_Ofun__left__comm__idem @ B @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ D ) @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(2640,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(1243,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ C @ B ) ) @ ( c_Predicate_OPowp @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__mono) ).
thf(5943,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ C @ B ) ) @ ( c_Predicate_OPowp @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(570,axiom,
! [A: $i] :
( ( hAPP @ ( c_Set_OPow @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__empty) ).
thf(3437,plain,
! [A: $i] :
( ( hAPP @ ( c_Set_OPow @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__is__inj) ).
thf(4702,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) @ A ) )
<=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
thf(5542,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) @ A ) )
=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) )
& ( ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(352,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(2563,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I3_J) ).
thf(3924,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1252,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ H @ G @ F @ E ) @ D )
= ( hAPP @ ( c_Fun_Ocomp @ C @ G @ F @ B ) @ A ) )
=> ! [I: $i] :
( ( hAPP @ E @ ( hAPP @ D @ I ) )
= ( hAPP @ B @ ( hAPP @ A @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(5986,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ H @ G @ F @ E ) @ D )
= ( hAPP @ ( c_Fun_Ocomp @ C @ G @ F @ B ) @ A ) )
=> ! [I: $i] :
( ( hAPP @ E @ ( hAPP @ D @ I ) )
= ( hAPP @ B @ ( hAPP @ A @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(1111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ B @ D ) @ A ) @ C ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
thf(5494,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ B @ D ) @ A ) @ C ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).
thf(3212,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(1157,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD) ).
thf(5649,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(1097,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__caseI) ).
thf(5458,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).
thf(3854,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(1200,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(5789,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(1147,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
thf(5618,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(1737,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ F @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__UN) ).
thf(2690,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ F @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ~ ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(1463,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ~ ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ~ ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__iff) ).
thf(5183,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(465,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ A ) ) @ c_FunDef_Omax__weak ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmax__emptyI) ).
thf(2998,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ A ) ) @ c_FunDef_Omax__weak ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__irrefl) ).
thf(1565,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1046,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).
thf(5261,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(319,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(2436,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__insert) ).
thf(2238,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).
thf(4752,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(910,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
thf(4742,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(2615,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(974,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__right) ).
thf(4977,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(4423,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I5_J) ).
thf(3200,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert) ).
thf(1812,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(16233,plain,
$false,
inference(cvc4,[status(thm)],[5561,2612,2778,1995,3798,3666,2427,5205,3172,5385,5810,5659,3021,5437,4201,2452,4447,5422,1337,1411,5365,4835,1823,3053,4450,3345,4464,2109,4824,2072,3661,2412,2876,4183,3477,3698,5390,2463,3397,3830,5654,2595,5028,4728,1818,6014,5454,6063,3072,5718,2495,5173,5982,5669,4479,5501,1855,2077,4037,2976,4376,3317,5168,4500,2231,3858,4311,2644,3905,1522,5069,2395,2062,3377,3040,4391,2953,2590,5297,3460,4807,5878,5625,5405,2837,3498,4215,1971,1793,4408,6031,5348,6017,4747,4592,3429,4739,3365,2316,6089,2141,5701,4440,2901,5636,2042,1705,4543,5967,1426,3530,4090,1655,4011,3649,4026,5288,1867,2184,4638,5146,1872,1919,3253,5161,4294,4247,3562,2146,4980,1507,2360,1746,1835,3629,5740,2046,1914,1782,3502,5745,5921,4198,3140,1366,6102,5269,1904,4467,3597,5621,5024,4386,1391,1576,3730,5723,4916,5903,1359,1601,3466,5301,2400,4963,2067,1967,1709,4524,3195,3644,3275,4151,4224,4761,2708,3776,4349,1455,1832,3820,5553,1628,4238,4539,2698,1760,5883,3046,3689,6095,5759,1907,2501,6066,1511,3485,2682,1826,5640,3089,1992,3353,3803,2466,4428,3043,2745,2571,1800,4119,1479,4830,4141,4793,4967,1847,5231,2420,3840,5256,4353,5866,5214,5605,4862,4788,2169,1514,4179,5193,2373,1347,3919,5323,4928,5052,4675,3312,5851,1931,3951,2158,6098,4632,5727,1641,3708,2301,1815,2989,1362,2852,3231,4302,2388,3866,2829,3788,2456,1946,3524,2090,1373,1911,1682,2925,5914,5156,2254,2335,4696,4205,4988,5264,6002,5888,4173,3934,5084,2105,4072,1450,3075,5597,1632,4297,2469,4733,2259,4001,4820,3163,2650,1334,3527,5558,1864,1677,2034,4871,5135,4798,4556,5259,3771,3851,1447,3808,1345,1433,5665,4707,5328,5970,1696,5695,1928,5773,5401,2281,5643,3421,1622,4087,2979,1394,3157,5846,2137,5321,4307,4040,2002,3955,4643,1943,3588,4285,3606,5824,4588,4604,3450,3591,3301,1691,6047,2164,5142,5291,2093,3679,1604,2922,5961,2011,3097,6020,5751,2574,5411,1306,5017,1311,5862,2083,4031,4059,2382,2773,5281,4999,5122,3418,4925,6092,2409,1723,3827,6000,4397,4434,5044,5266,1666,4521,3233,2606,3154,3339,1343,2560,3972,1502,1751,5815,5754,1619,1370,5102,2986,3250,2132,2890,4160,2528,3471,4044,3286,5843,1883,1560,3948,2433,3137,5690,5460,4327,5551,6060,3028,5858,2741,4461,5769,3958,3191,4280,5492,3618,2628,4192,2670,1555,2332,2826,2820,1888,1296,4553,5534,1687,1457,2200,2609,4402,5113,2181,4942,3647,2112,1291,4316,5066,5714,2840,1772,1804,5798,1587,2631,4930,2638,3440,5475,5189,1592,2498,3782,3615,3482,5221,2377,2801,1953,5006,1375,2973,4486,2509,3102,5428,1672,3518,5583,3632,3746,4840,3078,3916,3941,3018,4898,1397,4263,1567,4951,3143,5075,5496,4389,4736,3573,4530,5941,5830,4518,5166,5818,1964,3000,2323,4983,5181,3407,4772,3094,4167,1461,4421,1424,5464,4545,2080,5786,1414,1842,5588,1584,4513,4744,1937,2172,4054,5662,2349,4867,4444,5905,3555,1644,4814,1612,2472,4621,4804,5576,1297,1974,2581,5683,1984,3333,4416,4846,3611,2519,5481,5374,5149,6033,1530,1539,2487,2598,4970,3743,5973,4244,3222,3540,2006,2566,3937,5766,4231,1852,2813,3115,5305,3247,3409,4135,3692,2052,1599,4902,1720,4259,3109,1979,2370,5479,5170,2203,3225,4212,4476,6011,1663,2617,4004,2423,2909,3755,4535,2546,4195,1779,5090,2057,1712,3999,2963,5737,2368,5419,3639,5417,2221,2189,2995,5126,5840,4995,1732,5679,4919,2176,1754,2585,5278,3491,3262,3289,5608,5525,3686,4489,2894,2121,2235,2144,6053,4131,6026,1680,5808,4116,3871,2149,3257,2717,1548,3985,5928,4503,2524,2376,3536,3547,3070,2970,1916,3504,2849,2981,5097,5698,3372,2048,2859,1784,4494,3811,5395,3240,2393,3086,1652,3081,3758,3283,2674,2016,1388,3272,4801,5050,5876,3604,4381,1520,3868,4758,5503,4946,2695,1488,2161,4096,5595,4149,4413,4764,5207,5703,4273,5997,3568,5432,6016,4537,3796,3023,5039,1669,3118,5033,3964,5363,3051,5471,4796,5011,2308,4837,3695,4099,2738,1635,4822,3594,4573,5086,1997,2166,5539,4854,1897,3719,5578,2311,2521,2119,2478,2624,1806,3779,2955,5054,4154,3160,2065,2679,4704,4228,2538,1408,2642,3815,3764,2415,5520,1894,2493,1524,4828,3515,4699,5631,5303,5827,5853,2284,2257,1589,5901,5880,3710,4958,2945,2856,4176,5616,1439,4203,5657,4541,5894,5994,2780,1821,1862,3006,2252,2553,2461,4684,5780,4635,5367,6004,1557,4009,2314,4833,4064,1630,3932,4985,4452,4277,2757,3034,5392,1838,5318,6080,2289,2647,3480,1841,5931,3627,5216,2086,5646,3674,5725,2535,1364,1496,3348,6029,2867,2418,4933,5742,2962,5775,5094,3423,2481,2592,2244,3512,4497,4067,5326,4890,3876,2693,4209,4481,2506,3380,1562,4084,6083,5435,5688,4394,5528,1905,3981,3146,1509,3921,2846,1958,5652,3571,4405,2914,3031,2107,5886,4458,3576,2318,3206,5757,2037,2927,3975,1990,4859,2684,3292,2899,5358,5133,4812,1551,2942,6069,1961,3913,3112,2661,5484,5592,5523,3209,5446,3988,2513,1845,4749,5452,5047,5716,3737,1770,4360,5514,3507,5602,5111,5388,2060,4939,1400,5399,2192,4673,5499,3260,2588,4922,1647,3228,4641,4961,2386,5079,4324,4630,1499,3642,4905,1300,2920,6037,3722,5912,4222,3026,3655,3544,5152,4241,2044,1579,3715,2569,4437,1790,6036,4190,3818,3885,3823,2337,5030,2128,5154,5203,3623,3412,2247,1934,3488,3107,5675,1702,4143,5685,4342,2939,3961,4257,1849,3652,3415,6073,5628,4133,2992,4624,4611,3356,5613,5240,2357,2843,1485,2711,1504,4431,4235,6086,4093,2722,2807,5100,2458,1649,4851,3067,2870,5536,3533,3874,2347,3725,1734,5771,3168,1940,1421,3400,3584,4651,5490,3565,2088,5749,1459,3092,1685,2885,4944,4656,3188,5510,2215,5934,1517,2490,4102,3320,2305,5124,4170,1289,1453,5860,5332,2658,2775,4730,4678,4913,6077,4250,3336,3003,3368,4710,3864,1385,1674,2855,1639,5008,2406,4681,5191,5800,4126,2823,4715,3104,3991,6023,5813,5228,2026,2526,4527,4900,2152,3978,2796,3879,5692,5837,2362,1607,3552,5336,5864,5963,1491,3181,2384,2475,2912,4321,3267,5109,5072,3351,5869,3993,5590,2095,4074,5517,2294,5672,1444,1442,2917,4372,3761,2287,2102,3785,1546,1625,3264,3521,1527,4885,4367,3469,3658,2930,2218,4114,4399,4687,2155,4378,4809,2983,2719,4254,3733,3601,2233,4719,6050,5430,3837,2604,4841,1986,2008,1303,5477,5371,2050,4357,4491,1757,3203,4455,3309,3015,4029,1314,5462,5441,5339,6040,2668,1610,3805,1436,4146,2751,2800,3897,4051,4755,3560,4895,2186,3558,5990,4007,5105,4157,1693,2070,5586,3323,2714,3426,1891,4865,4442,4034,3843,5200,4318,1742,5803,2430,1532,5806,5140,2265,5581,4484,5623,4345,5473,5344,2241,5945,4848,3362,2810,4129,1829,5061,1976,5975,1357,4506,2583,5681,4410,4659,3538,5468,3939,5891,5354,2687,2864,3740,1880,1431,2484,1885,3494,3753,2754,4627,2074,2832,5569,4056,5293,2470,3669,1331,3474,2672,2640,5943,3437,4702,5542,2563,3924,5986,5494,3212,5649,5458,3854,5789,5618,1737,2690,1463,5183,2998,1565,5261,2436,2238,4752,4742,2615,4977,4423,3200,1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW358+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 22:04:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 1.02/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.74/1.40 % [INFO] Parsing done (502ms).
% 2.74/1.41 % [INFO] Running in sequential loop mode.
% 2.98/1.59 % [INFO] eprover registered as external prover.
% 2.98/1.59 % [INFO] cvc4 registered as external prover.
% 2.98/1.60 % [INFO] Scanning for conjecture ...
% 4.34/1.96 % [INFO] Found a conjecture and 5227 axioms. Running axiom selection ...
% 6.88/3.05 % [INFO] Axiom selection finished. Selected 1286 axioms (removed 3941 axioms).
% 8.78/3.89 % [INFO] Problem is first-order (TPTP FOF).
% 9.09/3.94 % [INFO] Type checking passed.
% 9.09/3.94 % [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 ...
% 97.67/29.56 % External prover 'cvc4' found a proof!
% 97.67/29.57 % [INFO] Killing All external provers ...
% 97.67/29.57 % Time passed: 29056ms (effective reasoning time: 28152ms)
% 97.67/29.57 % 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)>
% 97.67/29.58 % Axioms used in derivation (1286): fact_wf__not__refl, fact_insert__partition, fact_le__SucI, fact_UN__simps_I3_J, fact_insertCI, fact_Union__upper, arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice, fact_Int__lower1, fact_sequence__trans, fact_pos__union__def, fact_Sigma__Un__distrib1, fact_diff__0__eq__0, fact_inj__comp, fact_INT__simps_I6_J, fact_SUP1__I, fact_bex__empty, fact_Int__insert__left__if1, fact_card__partition, fact_Nat_Oadd__0__right, fact_Un__absorb1, fact_Sigma__Diff__distrib2, fact_converse__rtrancl__induct2, fact_singleton__iff, fact_wmin__emptyI, fact_Diff__insert__absorb, fact_card__image__le, fact_folding__image__simple__idem_Osubset__idem, fact_nat_Osimps_I3_J, fact_surj__f__inv__f, fact_le__imp__diff__is__add, fact_bij__betw__same__card, fact_Compl__UNIV__eq, fact_vimage__insert, fact_ImageE, fact_InterE, fact_Compl__UN, fact_folding__one_Osingleton, fact_New__DSequence_Opos__map__def, fact_finite__vimageI, fact_wf__not__sym, fact_finite__UN__I, fact_finite_Oequations_I1_J, fact_sup1I1, fact_Field__empty, fact_Sigma__def, fact_bij__imp__bij__inv, fact_inj__imp__surj__inv, fact_inf2I, fact_finite_OemptyI, fact_image__constant__conv, fact_pair__lessI2, fact_inj__on__diff__nat, fact_image__insert, fact_diff__add__inverse, fact_fun__left__comm__idem__insert, fact_minus__fold__remove, fact_card__gt__0__iff, fact_le__eq__less__or__eq, fact_nat__less__cases, fact_UnI1, fact_SUP1__iff, fact_image__Pow__mono, fact_curry__split, fact_trans__less__add1, fact_injD, fact_folding__image__simple__idem_Oin__idem, fact_comp__inj__on__iff, fact_accp_Oequations, fact_inf__INFI__fold__inf, fact_setsum__Un__nat, fact_card__Diff__subset__Int, fact_subset__UNIV, fact_nat__add__left__commute, fact_Compl__Times__UNIV1, fact_smax__insertI, fact_inv__into__into, fact_insert__iff, fact_INT__Un, fact_ex__bij__betw__finite__nat, fact_INT__extend__simps_I2_J, fact_one__is__add, fact_diff__le__mono2, fact_termination__basic__simps_I5_J, fact_insert__subset, fact_Inf__insert, fact_less__imp__le__nat, fact_card__Diff__subset, fact_Inter__insert, fact_finite__Collect__subsets, fact_greaterThan__iff, fact_double__complement, fact_Suc__mono, fact_less__nat__zero__code, fact_mono__Field, fact_setsum__diff__nat, fact_curry__def, fact_UNION__empty__conv_I1_J, fact_fun__left__comm__idem__remove, fact_add__leD1, fact_Times__Diff__distrib1, fact_INF1__iff, fact_Compl__Int, fact_Un__mono, fact_finite__INT, fact_n__less__m__mult__n, fact_fold__image__Un__one, fact_fun__left__comm_Ofold__equality, fact_prod_Orecs, fact_UN__finite__subset, fact_bij__betw__empty2, fact_Int__UNIV__right, fact_add__less__mono, fact_curry__conv, fact_UN__simps_I10_J, fact_INT__simps_I10_J, fact_image__Int, fact_diff__Suc__less, fact_insertI1, fact_mult__0, fact_vimage__UNIV, fact_Un__empty__left, fact_sup2I2, fact_pair__box_Oinject, fact_folding__one_Ounion__inter, fact_UNIV__not__empty, fact_ex__bij__betw__nat__finite, fact_inj__image__mem__iff, fact_image__add__atLeastLessThan, fact_nat__add__right__cancel, fact_quotient__diff1, fact_gr0__conv__Suc, fact_inj__on__the__inv__into, fact_Ex__inj__on__UNION__Sigma, fact_the__inv__f__f, fact_Int__left__commute, fact_assms_I1_J, fact_SigmaE2, fact_CollectI, fact_image__constant, fact_Un__insert__left, fact_Int__Union, fact_Un__Pow__subset, fact_comm__monoid__big_Oinfinite, fact_INT__D, fact_INFI__fold__inf, fact_finite__induct, fact_folding__image__simple_Oeq__fold__g, fact_max__ext__additive, fact_rtrancl_Ortrancl__refl, fact_SUP2__E, fact_zero__less__diff, fact_card_Oempty, fact_acc_Osimps, fact_atLeastLessThanSuc, fact_finite__range__imageI, fact_diff__diff__cancel, fact_inf__Inf__fold__inf, fact_o__eq__elim, fact_Compl__Un, fact_curryE, fact_empty__not__insert, fact_UN__extend__simps_I5_J, fact_image__vimage__eq, fact_mult__le__mono2, fact_Suc__diff__diff, fact_image__Int__subset, fact_Union__Int__subset, fact_Suc__le__mono, fact_Image__UN, conj_3, fact_inj__on__id, fact_image__UN, fact_finite__UnionD, fact_setsum__eq__Suc0__iff, fact_max__rpair__set, fact_inj__on__Un, help_c__COMBC__1, fact_atLeast__iff, fact_Int__UN__distrib, fact_surj__iff__all, fact_Un__UNIV__left, fact_UNION__empty__conv_I2_J, fact_mult__eq__self__implies__10, fact_Image__eq__UN, fact_wf__Int1, fact_le__neq__implies__less, fact_wf__less, fact_neg__single__def, fact_INT__greaterThan__UNIV, fact_folding_Oinsert, fact_comp__inj__on, fact_ComplD, fact_SUP__UN__eq2, fact_INT__E, fact_pred__equals__eq2, fact_Compl__eq__Diff__UNIV, fact_nat__add__left__cancel__less, fact_INT__subset__iff, fact_bij__is__inj, fact_o__apply, fact_INF__commute, fact_swap__inj__on, fact_rtrancl__mono, fact_image__Pow__surj, fact_rtrancl__subset__rtrancl, fact_finite__SigmaI, fact_folding__image_Ocong, fact_Powp__Pow__eq, fact_surj__image__vimage__eq, fact_split__paired__All, fact_Un__Diff__Int, fact_fun__left__comm_Ofun__left__comm, fact_inf1D2, fact_INT__lower, fact_inj__on__imageI2, fact_inv__into__image__cancel, fact_acc_OaccI, fact_insert__not__empty, fact_folding_Ocommute__left__comp, fact_UN__atLeast__UNIV, fact_prod_Osimps_I2_J, fact_bij__betw__inv__into, fact_Field__Union, fact_subset__Compl__self__eq, fact_smax__emptyI, fact_converse__rtranclE2, fact_image__image, fact_Int__insert__right, fact_Sigma__empty1, fact_type__definition_OAbs__inject, fact_inj__on__fun__updI, fact_Int__eq__Inter, fact_Diff__subset, fact_card__eq__UNIV__imp__eq__UNIV, fact_Field__Un, fact_sup__Un__eq2, fact_fun__left__comm_Ofold__graph__insertE, fact_folding_Oinsert__remove, fact_rev__ImageI, fact_folding__image__simple_Oremove, fact_bij__image__INT, fact_image__Un, fact_INT__simps_I3_J, fact_equalityD2, fact_finite__cartesian__productD1, fact_fold__graph_OemptyI, fact_image__Suc__atLeastLessThan, fact_type__definition_ORep__range, fact_finite__vimage__iff, fact_add__eq__if, fact_image__compose, fact_folding__one__idem_Oin__idem, fact_finite__Prod__UNIV, fact_folding__one_Oinsert, fact_finite__nat__set__iff__bounded__le, fact_Diff__idemp, fact_inf2D1, fact_mult__eq__1__iff, fact_o__id, fact_vimage__subset__eq, fact_bij__betw__subset, fact_finite__atLeastLessThan, fact_SUPR__apply, fact_gr0I, fact_predicate2D, fact_fold__graph__imp__finite, fact_bij__betw__id, fact_o__inv__o__cancel, fact_bot__empty__eq, fact_fun__left__comm_Ofold__graph__fold, fact_finite__UnI, fact_singleton__inject, fact_le__funD, fact_emptyE, fact_le__fun__def, fact_acc__subset, fact_DiffD2, fact_Int__empty__left, fact_UN__simps_I1_J, fact_inj__on__inv__into, fact_diff__le__self, fact_surj__iff, help_c__COMBS__1, fact_split__twice, fact_nat__mult__1__right, help_c__COMBI__1, fact_max__extp_Ointros, fact_fun__upd__same, fact_folding__image__simple__idem_Oinsert__idem, fact_less__eq__nat_Osimps_I1_J, fact_ord__less__eq__trans, fact_vimage__INT, fact_termination__basic__simps_I4_J, fact_le__iff__add, fact_wf__measure, fact_diff__commute, fact_diff__Suc__eq__diff__pred, fact_Compl__Diff__eq, fact_UN__Un__distrib, fact_Int__absorb2, fact_Diff__subset__conv, fact_less__add__eq__less, fact_wf__irrefl, fact_le__SUPI, fact_Image__Un, fact_INT__anti__mono, fact_add__lessD1, fact_add__le__mono1, fact_UN__extend__simps_I1_J, fact_Int__Diff, fact_DiffE, fact_quotient__is__empty, fact_inf__Int__eq, fact_folding__one__idem_Ounion__idem, fact_INF__INT__eq, fact_bij__betw__comp__iff2, fact_lessI, fact_finite__Un, fact_mem__splitE, fact_in__mono, fact_image__eq__fold__image, fact_card_Oinsert__remove, fact_Suc__less__SucD, fact_Babs__def, fact_vimage__if, fact_rtrancl__subset, fact_nat__eq__add__iff2, fact_mult__less__mono1, fact_subset__singletonD, fact_Diff__insert, fact_diff__less, fact_inj__on__iff__card__le, fact_card__image, fact_nat_Oinject, fact_max__ext_Osimps, fact_fun__left__comm__idem_Ofun__comp__idem, fact_union__fold__insert, fact_mem__splitI, fact_inj__on__Inter, fact_Int__assoc, fact_INF__leI, fact_not__add__less2, fact_less__or__eq__imp__le, fact_fold__image__def, fact_in__measure, fact_diff__card__le__card__Diff, fact_Int__Un__distrib, fact_INT__simps_I1_J, fact_top1I, fact_rev__image__eqI, fact_ball__empty, fact_ord_OatMost__iff, fact_Suc__leI, fact_folding__one_Oeq__fold_H, fact_wfE__pf, fact_subset__iff__psubset__eq, fact_finite__Collect__less__nat, fact_folding__one__idem_Oeq__fold__idem_H, fact_in__finite__psubset, fact_inj__on__contraD, fact_insert__is__Un, fact_wfP__def, fact_finite__imageD, fact_nat__mult__1, fact_diff__is__0__eq_H, fact_wf__subset, fact_rtrancl__Un__separator__converseE, fact_le__add2, fact_inj__on__strict__subset, fact_UN__extend__simps_I3_J, fact_finite__surj, fact_Suc__lessD, fact_Compl__disjoint2, fact_INT__simps_I7_J, fact_not__less__less__Suc__eq, fact_vimage__eq, fact_comp__cong, fact_fold__graph_H_Oequations_I1_J, fact_Image__subset, fact_Un__INT__distrib2, fact_UNIV__I, fact_pos__empty__def, fact_folding_Oempty, fact_Rep__Integ__inject, fact_finite__conv__nat__seg__image, fact_minus__nat_Odiff__0, fact_Int__insert__left, fact_ord_OgreaterThan__iff, fact_inj__on__diff, fact_fun__upd__comp, fact_UNION__eq__Union__image, fact_less__irrefl__nat, fact_Powp__def, fact_setsum__diff1__nat, fact_inj__on__Int, fact_Union__Un__distrib, fact_card__bij__eq, fact_fun__upd__idem, fact_folding__one_Oinsert__remove, fact_Suc__n__not__le__n, fact_fun__left__comm_Ofun__left__comm__apply, fact_not__less0, fact_card__psubset, fact_sup1I2, fact_inf1I, fact_Un__empty, fact_trans__less__add2, fact_less__Suc__eq__le, fact_INF__INT__eq2, fact_inj__vimage__image__eq, fact_INT__iff, fact_insert__code, fact_card_Oinsert, fact_fun__left__comm_Ofold__insert2, arity_fun__Complete__Lattice_Ocomplete__lattice, fact_add__diff__assoc, fact_card__eq__setsum, fact_acc__downwards, fact_Int__insert__right__if0, fact_Un__left__commute, fact_nat__diff__split, fact_wf__Int2, fact_Diff__triv, fact_add__leD2, fact_UN__extend__simps_I6_J, fact_card_Ounion__inter, fact_Pow__bottom, fact_UN__absorb, fact_max__ext_Ointros, fact_inf2E, fact_Compl__partition, fact_folding_Ounion__inter, fact_mult__le__cancel1, fact_o__eq__dest, fact_Pow__INT__eq, fact_type__definition_ORep, fact_diff__mult__distrib2, fact_New__DSequence_Oneg__single__def, fact_finite__empty__induct, fact_fun__upd__other, fact_inj__on__id2, fact_finite__Union, fact_rtrancl__Un__separatorE, fact_rtrancl__Un__rtrancl, fact_less__zeroE, fact_wf__empty, fact_termination__basic__simps_I2_J, fact_sup2I1, fact_one__le__mult__iff, fact_card__Suc__Diff1, fact_not__less__eq, fact_folding__one__idem_Ohom__commute, fact_INF2__D, fact_Union__image__eq, fact_folding__one__idem_Oinsert__idem, fact_insert__image, fact_nat_Osimps_I2_J, fact_finite__UN, fact_UN__extend__simps_I9_J, fact_insert__Diff__single, fact_bij__betw__comp__iff, fact_nat__neq__iff, fact_nat__1__eq__mult__iff, fact_card__Diff__insert, fact_fun__left__comm__idem_Ofun__left__idem, fact_fun__left__comm_Ofold__rec, fact_INT__extend__simps_I7_J, fact_one__less__mult, fact_Un__Int__crazy, fact_ex__in__conv, fact_vimageI2, fact_folding_Ocommute__comps_I1_J, fact_subset__insertI, fact_bij__comp, fact_UN__simps_I9_J, fact_add__mult__distrib2, fact_predicate1D, fact_less__not__refl3, fact_inf1E, fact_nat__diff__split__asm, fact_Diff__empty, fact_folding__image_Oreindex, fact_UN__extend__simps_I8_J, fact_finite__Field, conj_2, fact_finite__UNIV__card__ge__0, fact_inj__eq, fact_nat__add__left__cancel__le, fact_inv__o__cancel, fact_bij__is__surj, fact_atLeast__Suc, fact_inj__on__image__set__diff, fact_UN__I, fact_fun__upd__apply, fact_image__set__diff, fact_accp__subset, fact_InterI, fact_Times__Int__distrib1, fact_smin__insertI, arity_HOL__Obool__Orderings_Oord, fact_finite__Pow__iff, fact_vimage__Collect__eq, fact_Diff__partition, fact_Inter__def, fact_Un__Image, fact_max__ext__wf, fact_le__diff__conv, fact_finite__insert, fact_insert__absorb2, fact_diff__cancel, fact_card__def, fact_folding__one_Ounion__disjoint, fact_inj__on__Un__image__eq__iff, fact_greaterThan__Suc, fact_Inter__subset, fact_insertI2, fact_Diff__cancel, fact_less__Suc__eq__0__disj, fact_Times__subset__cancel2, fact_folding__idem_Oin__comp__idem, fact_folding__one__idem_Oidem, fact_equals0D, fact_le__Suc__eq, fact_Pow__def, fact_insert__absorb, fact_INT__insert__distrib, fact_subset__card__intvl__is__intvl, fact_empty__Collect__eq, fact_finite__fun__UNIVD1, fact_surj__id, fact_atLeast__Suc__greaterThan, fact_inj__image__eq__iff, fact_subset__insert, fact_card__insert, fact_rev__finite__subset, fact_vimage__def, fact_eqset__imp__iff, fact_le__add__diff__inverse2, fact_UN__simps_I4_J, fact_equalityD1, fact_fold__image__Un__Int, fact_pair__imageI, fact_inf2D2, fact_subset__image__iff, fact_nat__mult__assoc, fact_fun__left__comm__idem_Ofold__insert__idem2, fact_vimageI, fact_nat__mult__le__cancel1, fact_surj__Compl__image__subset, fact_Suc__mult__less__cancel1, fact_vimage__mono, fact_less__antisym, fact_split__Pair, fact_Inf__lower, fact_in__rtrancl__UnI, fact_Sup__binary, fact_splitI, fact_Inter__anti__mono, fact_le__INF__iff, fact_Un__Int__distrib2, fact_Suc__le__eq, fact_range__composition, fact_mult__cancel2, fact_Int__Un__distrib2, fact_converse__rtrancl__into__rtrancl, fact_Un__insert__right, fact_wfP__accp__iff, fact_image__eq__UN, fact_Diff__Int__distrib2, fact_folding__image__simple_Oinsert__remove, fact_diff__single__insert, fact_max__extp_Oequations, fact_finite__Diff__insert, fact_pos__single__def, fact_le__funE, fact_INT__constant, fact_nat__diff__add__eq2, fact_inj__on__def, fact_inj__on__iff, fact_UN__insert, fact_UN__extend__simps_I10_J, fact_Compl__iff, fact_less__add__Suc2, fact_Int__UN__distrib2, fact_Sigma__Diff__distrib1, fact_Suc__pred_H, fact_DiffD1, arity_Nat__Onat__Orderings_Oord, fact_finite__nat__set__iff__bounded, fact_finite__Inter, fact_bij__betw__imp__inj__on, fact_rtrancl__trans, fact_less__eq__Suc__le, fact_accp__wfPD, fact_less__by__empty, fact_Diff__Compl, fact_UnI2, fact_inv__id, fact_rp__inv__image__rp, fact_finite__Int, fact_Int__lower2, fact_insert__commute, fact_fun__upd__triv, fact_Diff__Int2, fact_fun__left__comm_Ofold__graph__insertE__aux, fact_subset__Un__eq, fact_less__imp__diff__less, fact_inj__singleton, fact_Inf__fold__inf, fact_inj__image__Compl__subset, fact_Compl__INT, fact_wmax__emptyI, fact_Int__absorb, fact_inv__image__comp, fact_folding__image__simple_Oinsert, fact_Union__insert, fact_UN__extend__simps_I2_J, fact_nat__mult__eq__cancel1, fact_Int__Union2, fact_fold__graph_Oequations_I1_J, fact_insert__inter__insert, fact_pair__box_Orecs, fact_range__ex1__eq, fact_finite__imageI, fact_Un__INT__distrib, fact_finite__Diff, fact_ord__le__eq__trans, fact_fold__image__UN__disjoint, fact_INT__extend__simps_I1_J, fact_all__not__in__conv, fact_fun__left__comm__idem_Ofold__insert__idem, fact_empty__is__image, fact_mlex__leq, fact_singleton__quotient, fact_vimage__code, fact_set__mp, fact_psubset__card__mono, fact_bij__betw__Disj__Un, fact_Times__Un__distrib1, fact_INT__extend__simps_I10_J, fact_UN__UN__finite__eq, fact_fun__left__comm_Ofold__insert__remove, fact_nat__mult__less__cancel1, fact_id__def, fact_add__is__1, fact_Image__Int__subset, fact_PowD, fact_folding_Ocommute__comp_H_H, fact_Inter__empty, fact_INT__extend__simps_I6_J, fact_linorder__neqE__nat, fact_mult__less__mono2, fact_accp__downward, fact_Image__singleton__iff, fact_vimage__Un, fact_diffs0__imp__equal, fact_Compl__Times__UNIV2, fact_card__ge__0__finite, fact_Diff__mono, fact_diff__diff__left, fact_UN__insert__distrib, fact_fun__upd__idem__iff, fact_Un__Diff__cancel, fact_psubsetD, fact_SigmaE, fact_fold__graph_H_Ointros_I1_J, fact_bex__Un, fact_UN__UN__flatten, fact_inj__image__subset__iff, fact_Sup__UNIV, fact_inj__iff, fact_le__Inf__iff, fact_diff__Suc__diff__eq2, fact_Times__eq__cancel2, fact_bex__UNIV, fact_ord_OlessThan__iff, fact_Suc__mult__cancel1, fact_inv__into__injective, fact_folding_Ocommute__left__comp_H_H, fact_UN__Times__distrib, fact_fold__graph_OinsertI, fact_card__insert__if, fact_card__Un__disjoint, fact_double__diff, fact_fun__left__comm_Ofold__fun__comm, fact_diff__diff__right, fact_UN__constant, fact_wf__acc__iff, arity_Nat__Onat__Groups_Ocomm__monoid__mult, fact_sup1CI, fact_CollectE, fact_subset__inj__on, fact_mem__Collect__eq, fact_Suc__le__lessD, fact_diff__add__assoc2, fact_Image__empty, fact_INT__Int__distrib, fact_set__eq__subset, fact_Sup__fold__sup, fact_sup2E, fact_Cantors__paradox, fact_Un__Int__assoc__eq, fact_not__add__less1, fact_bij__betw__id__iff, fact_SUP__le__iff, fact_psubset__trans, fact_vimage__Union, fact_Pair__inject, fact_Image__singleton, fact_image__INT, fact_finite__compl, fact_pred__subset__eq, fact_folding__one__idem_Osubset__idem, fact_nat__le__add__iff2, fact_Suc__inject, fact_Sigma__Int__distrib2, fact_o__inv__distrib, fact_INTER__UNIV__conv_I1_J, fact_folding_Ounion, fact_Suc__neq__Zero, fact_empty__iff, fact_vimage__Diff, fact_Pow__not__empty, arity_fun__Orderings_Oord, fact_equalityI, fact_subset__refl, fact_less__diff__conv, fact_ext, fact_folding__one_Oclosed, fact_Inf__binary, fact_inf1D1, fact_smin__emptyI, fact_acc__wfD, fact_eq__diff__iff, fact_vimage__ident, fact_UN__simps_I5_J, fact_fold__graph_H_Ointros_I2_J, fact_Pow__iff, fact_card__eq__0__iff, fact_inf__Int__eq2, fact_folding__idem_Oinsert__idem, fact_card__mono, fact_diff__less__Suc, fact_add__eq__self__zero, fact_image__vimage__subset, fact_Diff__Int, fact_UN__simps_I8_J, fact_Cantor__Bernstein, fact_Sigma__Int__distrib1, fact_bij__vimage__eq__inv__image, fact_nat__less__add__iff1, fact_split__eta, fact_assms_I3_J, fact_setsum__eq__1__iff, fact_sup__Un__eq, fact_prod__caseI, fact_mult__is__0, fact_nat__add__left__cancel, fact_Suc__diff__1, fact_mult__le__cancel2, fact_Image__closed__trancl, fact_endo__inj__surj, fact_INT__simps_I5_J, fact_INF2__E, fact_fun__upd__upd, fact_mult__le__mono, fact_Int__commute, fact_Collect__def, fact_wfI__pf, fact_rtrancl__induct2, fact_nat__seg__image__imp__finite, fact_n__not__Suc__n, fact_nat__le__linear, fact_mem__splitI2, fact_inv__into__f__f, fact_Collect__mem__eq, fact_UN__empty2, fact_UN__extend__simps_I7_J, fact_vimage__subsetD, fact_finite__subset__image, fact_INT__simps_I9_J, fact_max__strict__def, help_c__COMBB__1, fact_rangeI, fact_le__add__diff, fact_INT__extend__simps_I4_J, fact_folding__idem_Ounion__idem, fact_insert__ident, fact_Int__Collect__mono, fact_INT__extend__simps_I3_J, fact_wf__iff__no__infinite__down__chain, fact_nat__0__less__mult__iff, fact_folding__image__simple_Ounion__inter, fact_subset__empty, fact_subset__insert__iff, fact_rtrancl__Un__subset, fact_finite__vimageD, fact_add__mult__distrib, fact_ball__UN, fact_card__inj__on__le, fact_fun__left__comm_Ofun__comp__comm, fact_inj__on__imageI, fact_inj__on__INTER, fact_add__Suc, fact_diff__add__assoc, fact_Inter__Un__subset, fact_wf__eq__minimal, fact_Powp__mono, fact_fun__left__comm__idem_Ofun__left__comm__idem__apply, fact_nat__le__add__iff1, fact_folding_Ocommute__left__comp_H, fact_mult__less__cancel1, fact_curryD, fact_Diff__disjoint, fact_card__Un__Int, fact_inj__on__imp__bij__betw, fact_add__gr__0, fact_image__is__empty, fact_SUP__UN__eq, fact_add__diff__assoc2, fact_image__diff__subset, fact_mlex__less, fact_psubset__imp__subset, fact_Un__absorb, fact_vimage__Int, fact_singletonE, fact_Int__Inter__image, fact_diff__less__mono2, fact_IntD2, fact_quotientI, fact_UN__Pow__subset, fact_min__rpair__set, fact_set__rev__mp, fact_Diff__eq, fact_DiffI, fact_ex__nat__less__eq, fact_ord_OgreaterThanLessThan__iff, fact_the__inv__into__into, fact_mem__Sigma__iff, fact_acc__downwards__aux, fact_sup__SUPR__fold__sup, fact_setsum__SucD, fact_Sup__insert, fact_Compl__subset__Compl__iff, fact_UN__upper, fact_diff__mult__distrib, fact_card__insert__disjoint, fact_eq__mem__trans, fact_Compl__anti__mono, fact_Int__mono, fact_inj__on__iff__eq__card, fact_ord_OatLeastLessThan__iff, fact_Suc__eq__plus1__left, fact_trancl__subset__Sigma__aux, fact_Zero__not__Suc, fact_SigmaI, fact_Un__empty__right, fact_inv__f__f, fact_wf__insert, fact_Inter__lower, fact_pigeonhole, fact_Union__disjoint, fact_diff__less__mono, fact_inv__inv__eq, fact_Suc__leD, fact_Pow__mono, fact_rev__predicate2D, fact_the__inv__into__comp, fact_mult__Suc, fact_card_Ounion__inter__neutral, fact_less__trans__Suc, fact_folding__image_Oeq__fold, fact_left__add__mult__distrib, fact_id__o, fact_Un__absorb2, fact_Int__insert__right__if1, fact_image__surj__f__inv__f, fact_Union__mono, fact_INF1__D, fact_vimage__empty, fact_Pow__UNIV, fact_New__DSequence_Opos__empty__def, fact_less__eq__Suc__le__raw, fact_Int__Collect, fact_UN__simps_I2_J, fact_Diff__UNIV, fact_Nat_Odiff__diff__eq, fact_le__refl, fact_nat__add__assoc, fact_insert__times__insert, fact_vimage__UN, fact_subset__insertI2, fact_less__not__refl2, fact_fold__image__distrib, fact_Inf__UNIV, fact_inj__fun, fact_le__add1, fact_mult__cancel1, fact_INT__empty, fact_SUP2__iff, fact_trans__le__add2, fact_Diff__Int__distrib, fact_accp_Osimps, fact_UN__iff, fact_folding_Oremove, fact_UnCI, fact_Int__absorb1, fact_insert__Diff, fact_add__is__0, fact_Diff1__fold__graph, fact_SigmaD2, fact_folding__image__simple__idem_Ounion__idem, fact_atLeastLessThan__singleton, fact_card__Diff2__less, fact_le__imp__less__Suc, fact_Compl__partition2, conj_1, fact_image__split__eq__Sigma, fact_fold__Un__disjoint, fact_bot2E, fact_Union__def, fact_comm__monoid__big_OF__eq, fact_K__record__comp, fact_Suc__mult__le__cancel1, fact_less__add__Suc1, fact_all__nat__less__eq, fact_finite__Collect__le__nat, fact_o__def, fact_less__fun__def, fact_rev__predicate1D, fact_One__nat__def, fact_nat__diff__add__eq1, fact_termination__basic__simps_I3_J, fact_image__inv__into__cancel, fact_Rep__Integ__induct, fact_bij__betw__def, fact_card__Diff1__le, fact_inv__f__eq, fact_wf__no__infinite__down__chainE, fact_folding__image__simple_Oempty, fact_folding__one_Oremove, fact_Pow__insert, fact_ball__Un, fact_bij__betw__the__inv__into, fact_o__eq__dest__lhs, fact_Un__upper1, fact_folding_Ocommute__comp, fact_UN__simps_I7_J, fact_nat__eq__add__iff1, fact_Inter__UNIV, fact_mult__le__mono1, fact_diff__self__eq__0, fact_card__quotient__disjoint, fact_accp__acc__eq, fact_Zero__neq__Suc, fact_greaterThan__0, fact_INT__greatest, fact_INF__subset, fact_diff__cancel2, fact_Sigma__Union, fact_InterD, fact_bij__betw__empty1, fact_equalityE, fact_CollectD, fact_nat__less__add__iff2, fact_split__curry, fact_Pair__eq, fact_Suc__eq__plus1, fact_Union__empty, fact_finite__cartesian__productD2, fact_Collect__empty__eq, fact_image__iff, fact_rtrancl_Ortrancl__into__rtrancl, fact_inj__transfer, fact_Int__insert__left__if0, fact_split__conv, fact_UN__finite2__subset, fact_finite__Diff2, fact_vimage__eq__UN, fact_subset__psubset__trans, fact_UN__Un, fact_INF1__E, fact_Un__UNIV__right, fact_empty__subsetI, fact_insert__Diff__if, fact_UNIV__Times__UNIV, fact_diff__add__0, fact_finite__cartesian__product, fact_card__seteq, fact_finite__fun__UNIVD2, fact_the__inv__into__onto, fact_splitD, fact_Suc__diff__le, fact_INT__absorb, fact_Un__Inter, fact_split__weak__cong, fact_bot__empty__eq2, fact_insert__mono, fact_ord__eq__less__trans, fact_card_Oremove, fact_INF2__I, fact_Sigma__Un__distrib2, fact_ord_OgreaterThanAtMost__iff, fact_le0, fact_ex__least__nat__less, fact_Suc__pred, fact_gr__implies__not0, fact_bijI, fact_folding__idem_Oidem__comp, fact_nat__mult__eq__1__iff, fact_not__less__eq__eq, fact_n__less__n__mult__m, fact_less__not__refl, fact_folding_Oeq__fold, fact_fun__upd__def, fact_le__diff__conv2, fact_Un__Diff__cancel2, fact_the__inv__into__f__eq, fact_INT__extend__simps_I8_J, fact_card_Oeq__fold__g, fact_f__the__inv__into__f, fact_le__trans, fact_diff__Suc__diff__eq1, fact_wf__mlex, fact_equalityCE, fact_r__into__rtrancl, fact_finite__subset__induct, fact_atLeast__0, fact_UN__o, fact_vimage__const, fact_Int__UNIV__left, fact_fun__upd__twist, fact_id__apply, fact_folding__image__simple_Ounion__inter__neutral, fact_finite_OinsertI, fact_fun__left__comm_Ofold__graph__determ, help_c__COMBK__1, fact_Un__iff, fact_rtrancl__idemp, fact_UN__singleton, fact_IntI, fact_inj__on__add__nat, fact_bij__image__Collect__eq, fact_Un__Diff, fact_quotientE, fact_finite__less__ub, fact_fold__image__Sigma, fact_fun__left__comm_Ofold__insert, fact_Inter__image__eq, fact_psubset__insert__iff, fact_INTER__eq__Inter__image, fact_type__definition_OAbs__inverse, fact_comp__surj, fact_Diff__insert2, fact_image__eqI, fact_subsetD, fact_Compl__disjoint, fact_Diff__Un, fact_less__Suc__eq, fact_nat__add__commute, fact_bij__betw__combine, fact_inv__into__comp, fact_Suc__less__eq, fact_fold__image__empty, fact_swap__product, fact_eq__card__imp__inj__on, fact_card__SigmaI, fact_psubset__eq, fact_add__leE, fact_finite__quotient, fact_PowI, fact_INFI__apply, fact_range__eqI, fact_card__cartesian__product__singleton, fact_sup1E, fact_diff__Suc__1, fact_image__ident, fact_the__inv__into__f__f, fact_Int__empty__right, fact_zero__less__Suc, fact_card_Oneutral, fact_card__atLeastLessThan, fact_folding__idem_Osubset__comp__idem, fact_subset__Pow__Union, fact_mult_Ocomm__neutral, fact_insertE, fact_inj__Suc, fact_New__DSequence_Opos__single__def, fact_bij__image__Compl__eq, fact_Union__Pow__eq, fact_assms_I4_J, fact_atLeastLessThan0, fact_sup__Sup__fold__sup, fact_acc__downward, fact_image__Union, fact_nat__mult__commute, fact_eq__imp__le, fact_finite__surj__inj, fact_Union__UNIV, fact_inv__into__f__eq, fact_image__mono, fact_diff__add__inverse2, fact_infinite__UNIV__nat, fact_plus__nat_Oadd__0, fact_card__Diff1__less, fact_card__Suc__eq, fact_Pow__Int__eq, fact_max__extp_Osimps, fact_empty__Diff, fact_Sup__singleton, fact_type__definition_ORep__inject, fact_Inf__empty, fact_le__SucE, fact_le__less__Suc__eq, fact_atLeastLessThan__add__Un, fact_inj__onD, fact_finite__equiv__class, fact_INT__simps_I8_J, fact_inv__into__inv__into__eq, fact_card__cartesian__product, fact_f__inv__into__f, fact_Inter__Un__distrib, fact_trans__le__add1, fact_eqelem__imp__iff, fact_type__definition_OAbs__image, fact_card__infinite, fact_pred__equals__eq, fact_Diff__iff, fact_folding__image__simple_Ounion__disjoint, fact_psubset__subset__trans, fact_Un__least, fact_bij__id, fact_curryI, fact_Sup__le__iff, fact_ComplI, fact_neq0__conv, fact_Sigma__mono, fact_quotient__is__empty2, fact_Suc__n__not__n, fact_pos__not__random__dseq__def, fact_o__eq__id__dest, fact_mult__0__right, fact_subset__trans, fact_empty__fold__graphE, fact_IntE, fact_fold__image__1, fact_le__antisym, fact_Un__commute, fact_Compl__eq__Compl__iff, fact_Image__iff, fact_UN__extend__simps_I4_J, fact_folding__image_Odistrib, fact_New__DSequence_Opos__union__def, fact_INT__simps_I4_J, fact_diff__le__mono, fact_wfP__wf__eq, fact_INT__simps_I2_J, fact_card__Diff__singleton, fact_pair__lessI1, fact_pair__box_Osimps_I2_J, fact_le__0__eq, fact_assms_I2_J, fact_mult__Suc__right, fact_Int__greatest, fact_finite__UNIV__surj__inj, fact_folding_Ocommute__comp_H, fact_Sup__empty, fact_diff__is__0__eq, fact_Un__upper2, fact_fun__upd__image, fact_INT__insert, fact_nat__mult__eq__cancel__disj, fact_Int__left__absorb, fact_termination__basic__simps_I1_J, fact_less__iff__Suc__add, fact_finite__subset, fact_UN__finite2__eq, fact_mult__less__cancel2, fact_finite__UNIV__inj__surj, fact_wf__asym, fact_Times__empty, fact_not__psubset__empty, fact_SUP2__I, fact_fold__empty, fact_SigmaD1, fact_SUPR__fold__sup, fact_IntD1, conj_0, fact_INT__extend__simps_I9_J, fact_SUP__commute, fact_le__add__diff__inverse, fact_Int__iff, fact_inj__on__insert, fact_Un__left__absorb, fact_vimage__singleton__eq, fact_add__le__mono, fact_less__Suc0, fact_Sup__upper, fact_add__diff__inverse, fact_Un__eq__Union, fact_UnionE, fact_iso__tuple__UNIV__I, fact_le__diff__iff, fact_bij__betw__imp__surj, fact_mem__def, fact_UnionI, fact_INT__extend__simps_I5_J, fact_Rep__Integ, fact_vimageD, fact_Un__Int__distrib, fact_ord__eq__le__trans, fact_UnE, fact_Field__insert, fact_less__diff__iff, fact_UN__simps_I6_J, fact_diff__Suc__Suc, fact_vimage__subsetI, fact_image__empty, fact_bij__betw__finite, fact_nat__less__le, fact_image__minus__const__atLeastLessThan__nat, fact_Image__INT__subset, fact_type__definition_ORep__inverse, fact_le__square, fact_wf__pair__less, fact_wf__finite__psubset, fact_mult__eq__if, fact_bij__betw__trans, fact_pred__subset__eq2, fact_card__insert__le, fact_ComplE, fact_less__SucE, fact_le__cube, fact_vimage__Compl, fact_INTER__UNIV__conv_I2_J, fact_add__less__mono1, fact_card__Diff__singleton__if, fact_UN__subset__iff, fact_sup2CI, fact_Un__Union__image, fact_inj__on__image__Int, fact_disjoint__eq__subset__Compl, fact_fold__graph_H_Oequations_I2_J, fact_bij__def, fact_INF__const, fact_o__assoc, fact_Image__mono, fact_Pow__top, fact_wfP__subset, fact_inj__on__empty, fact_not__acc__down, fact_doubleton__eq__iff, fact_insert__Diff1, fact_quotient__def, fact_SUP__const, fact_setsum__eq__0__iff, fact_vimage__id, fact_vimage__compose, fact_bot__nat__def, fact_Un__assoc, fact_INF2__iff, fact_Sigma__empty2, fact_add__Suc__shift, fact_Inf__singleton, fact_less__SucI, fact_Suc__not__Zero, fact_folding__image__simple__idem_Oidem, fact_surj__imp__inj__inv, fact_folding__idem_Oidem__left__comp, fact_Suc__lessI, fact_Pow__empty, fact_add__Suc__right, fact_mult__1, fact_image__id, fact_inj__on__iff__surj, fact_BIJ, fact_splitD_H, fact_Compl__empty__eq, fact_SUP__subset, fact_image__inv__f__f, fact_Rep__Integ__cases, fact_ord_OatLeast__iff, fact_max__extp__max__ext__eq, fact_quotient__empty, fact_imageI, fact_disjoint__iff__not__equal
% 97.67/29.58 % No. of inferences in proof: 2576
% 97.67/29.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 29056 ms resp. 28152 ms w/o parsing
% 99.81/30.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 100.01/30.39 % [INFO] Killing All external provers ...
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