TSTP Solution File: SWW374+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW374+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 12:23:39 EDT 2023
% Result : Theorem 16.49s 5.13s
% Output : Refutation 17.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 403
% Syntax : Number of formulae : 701 ( 168 unt; 107 typ; 0 def)
% Number of atoms : 1548 ( 545 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 9346 ( 226 ~; 67 |; 221 &;8166 @)
% ( 80 <=>; 586 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 252 ( 252 >; 0 *; 0 +; 0 <<)
% Number of symbols : 109 ( 107 usr; 18 con; 0-6 aty)
% Number of variables : 2503 ( 0 ^;2439 !; 64 ?;2503 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Com_OWT_type,type,
c_Com_OWT: $i ).
thf(c_Option_Othe_type,type,
c_Option_Othe: $i > $i ).
thf(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
thf(c_Com_Obody_type,type,
c_Com_Obody: $i ).
thf(v_pn_type,type,
v_pn: $i ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i ).
thf(tc_Option_Ooption_type,type,
tc_Option_Ooption: $i > $i ).
thf(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: $i > $i ).
thf(c_Map_Omap__le_type,type,
c_Map_Omap__le: $i > $i > $i > $i > $o ).
thf(c_Option_Ooption_ONone_type,type,
c_Option_Ooption_ONone: $i > $i ).
thf(c_Map_Oran_type,type,
c_Map_Oran: $i > $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
thf(c_Map_Orestrict__map_type,type,
c_Map_Orestrict__map: $i > $i > $i > $i > $i ).
thf(c_member_type,type,
c_member: $i > $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(c_Map_Omap__add_type,type,
c_Map_Omap__add: $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_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(c_Finite__Set_Ofold_type,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(c_Map_Omap__comp_type,type,
c_Map_Omap__comp: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Map_Odom_type,type,
c_Map_Odom: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofold__graph_type,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(class_Nat_Osize_type,type,
class_Nat_Osize: $i > $o ).
thf(class_Enum_Oenum_type,type,
class_Enum_Oenum: $i > $o ).
thf(c_Finite__Set_Ofolding__image__simple_type,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold__image_type,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(class_HOL_Oequal_type,type,
class_HOL_Oequal: $i > $o ).
thf(c_Finite__Set_Ofolding__image__simple__idem_type,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Com_Ocom_OCond_type,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i > $i ).
thf(c_Map_Omap__of_type,type,
c_Map_Omap__of: $i > $i > $i ).
thf(c_Com_Ocom_OWhile_type,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(c_Com_Ocom_OSemi_type,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Com_Ocom_OLocal_type,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(c_Predicate_Oconversep_type,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i ).
thf(c_Natural_Oevalc_type,type,
c_Natural_Oevalc: $i > $i > $i > $o ).
thf(c_Com_Ocom_OCall_type,type,
c_Com_Ocom_OCall: $i > $i > $i > $i ).
thf(c_New__DSequence_Oneg__union_type,type,
c_New__DSequence_Oneg__union: $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Oappend_type,type,
c_Lazy__Sequence_Oappend: $i > $i > $i > $i ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_Com_OWT__bodies_type,type,
c_Com_OWT__bodies: $o ).
thf(c_Predicate_Opred__comp_type,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Natural_Oevaln_type,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(c_Typedef_Otype__definition_type,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_Option_Oset_type,type,
c_Option_Oset: $i > $i > $i ).
thf(c_Wellfounded_OwfP_type,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(c_Finite__Set_Ofolding__one__idem_type,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_New__Random__Sequence_Opos__empty_type,type,
c_New__Random__Sequence_Opos__empty: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__empty_type,type,
c_New__DSequence_Opos__empty: $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_type,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequivp_type,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(c_Finite__Set_Ofold1_type,type,
c_Finite__Set_Ofold1: $i > $i > $i ).
thf(c_Hilbert__Choice_OEps_type,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(c_Big__Operators_Ocomm__monoid__big_type,type,
c_Big__Operators_Ocomm__monoid__big: $i > $i > $i > $i > $i > $o ).
thf(c_Enum_Oenum__class_Oenum__all_type,type,
c_Enum_Oenum__class_Oenum__all: $i > $i ).
thf(c_Enum_Oenum__class_Oenum__ex_type,type,
c_Enum_Oenum__class_Oenum__ex: $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_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_Divides_Odivmod__nat__rel_type,type,
c_Divides_Odivmod__nat__rel: $i > $i > $i ).
thf(c_Divides_Odivmod__nat_type,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThan_type,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(c_fNot_type,type,
c_fNot: $i ).
thf(c_fimplies_type,type,
c_fimplies: $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_Big__Operators_Osemilattice__big_type,type,
c_Big__Operators_Osemilattice__big: $i > $i > $i > $o ).
thf(c_FunDef_Oreduction__pair_type,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Orp__inv__image_type,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(c_Predicate_OPowp_type,type,
c_Predicate_OPowp: $i > $i > $i ).
thf(c_New__DSequence_Oneg__map_type,type,
c_New__DSequence_Oneg__map: $i > $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Ohb__map_type,type,
c_Lazy__Sequence_Ohb__map: $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Ohb__single_type,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(c_Predicate_ODomainP_type,type,
c_Predicate_ODomainP: $i > $i > $i > $i ).
thf(c_fdisj_type,type,
c_fdisj: $i ).
thf(c_Predicate_ORangeP_type,type,
c_Predicate_ORangeP: $i > $i > $i > $i ).
thf(c_fTrue_type,type,
c_fTrue: $i ).
thf(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
thf(c_Com_Obodies_type,type,
c_Com_Obodies: $i ).
thf(c_SetInterval_Oord_OatLeastLessThan_type,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_fconj_type,type,
c_fconj: $i ).
thf(c_SetInterval_Oord_OatLeast_type,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(c_fFalse_type,type,
c_fFalse: $i ).
thf(c_SetInterval_Oord_OgreaterThanLessThan_type,type,
c_SetInterval_Oord_OgreaterThanLessThan: $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_SetInterval_Oord_OgreaterThanAtMost_type,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_type,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_type,type,
c_SetInterval_Oord_OlessThan: $i > $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_Nitpick_Opair__box_Opair__box__case_type,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Oempty_type,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(v_c_type,type,
v_c: $i ).
thf(c_Int_ORep__Integ_type,type,
c_Int_ORep__Integ: $i ).
thf(c_New__Random__Sequence_Oneg__union_type,type,
c_New__Random__Sequence_Oneg__union: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Predicate_Oreflp_type,type,
c_Predicate_Oreflp: $i > $i > $o ).
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_SetInterval_Oord_OatLeastAtMost_type,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
<=> ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I9_J) ).
thf(1337,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
=> ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A ) )
& ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ~ ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WTs__elim__cases_I4_J) ).
thf(1168,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ~ ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(269,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(1454,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ A ) @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OWhileFalse) ).
thf(893,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ A ) @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OBody) ).
thf(1211,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) )
= ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).
thf(1005,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)],[157]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ B @ A @ E ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Ointros) ).
thf(1401,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ B @ A @ E ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(1422,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)],[259]) ).
thf(38,axiom,
! [A: $i] : ( class_Nat_Osize @ ( tc_Option_Ooption @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Nat_Osize) ).
thf(449,plain,
! [A: $i] : ( class_Nat_Osize @ ( tc_Option_Ooption @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Oequations) ).
thf(1173,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__le @ D @ C @ B @ ( c_Map_Omap__add @ D @ C @ B @ A ) )
<=> ( ( c_Map_Omap__add @ D @ C @ B @ A )
= ( c_Map_Omap__add @ D @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__le__iff__map__add__commute) ).
thf(408,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Map_Omap__le @ D @ C @ B @ ( c_Map_Omap__add @ D @ C @ B @ A ) )
=> ( ( c_Map_Omap__add @ D @ C @ B @ A )
= ( c_Map_Omap__add @ D @ C @ A @ B ) ) )
& ( ( ( c_Map_Omap__add @ D @ C @ B @ A )
= ( c_Map_Omap__add @ D @ C @ A @ B ) )
=> ( c_Map_Omap__le @ D @ C @ B @ ( c_Map_Omap__add @ D @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
thf(977,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)],[153]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_New__Random__Sequence_Opos__union @ F @ E @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__union @ F @ ( hAPP @ ( hAPP @ ( hAPP @ E @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__union__def) ).
thf(1158,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)],[191]) ).
thf(74,axiom,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(582,plain,
c_Com_OWT__bodies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__le @ D @ C @ B @ A )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( c_Map_Odom @ D @ C @ B ) ) )
=> ( ( hAPP @ B @ E )
= ( hAPP @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__le__def) ).
thf(762,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Map_Omap__le @ D @ C @ B @ A )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( c_Map_Odom @ D @ C @ B ) ) )
=> ( ( hAPP @ B @ E )
= ( hAPP @ A @ E ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( c_Map_Odom @ D @ C @ B ) ) )
=> ( ( hAPP @ B @ E )
= ( hAPP @ A @ E ) ) )
=> ( c_Map_Omap__le @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( C = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).
thf(878,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)],[130]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Map_Omap__comp @ G @ F @ E @ D @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) )
<=> ? [H: $i] :
( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ H ) )
& ( ( hAPP @ D @ H )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__Some__iff) ).
thf(440,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( c_Map_Omap__comp @ G @ F @ E @ D @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) )
=> ? [H: $i] :
( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ H ) )
& ( ( hAPP @ D @ H )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) )
& ( ? [H: $i] :
( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ H ) )
& ( ( hAPP @ D @ H )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) )
=> ( ( c_Map_Omap__comp @ G @ F @ E @ D @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(260,axiom,
class_Nat_Osize @ tc_Com_Ocom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com__Ocom__Nat_Osize) ).
thf(1426,plain,
class_Nat_Osize @ tc_Com_Ocom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold_H) ).
thf(384,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)],[22]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all) ).
thf(1137,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__le @ E @ D @ C @ B )
=> ( ( c_Map_Omap__le @ E @ D @ B @ A )
=> ( c_Map_Omap__le @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__le__trans) ).
thf(472,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__le @ E @ D @ C @ B )
=> ( ( c_Map_Omap__le @ E @ D @ B @ A )
=> ( c_Map_Omap__le @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(237,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Com_Opname ) @ v_pn ) @ ( c_Map_Odom @ tc_Com_Opname @ tc_Com_Ocom @ c_Com_Obody ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(1327,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Com_Opname ) @ v_pn ) @ ( c_Map_Odom @ tc_Com_Opname @ tc_Com_Ocom @ c_Com_Obody ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Option_Othe @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the_Osimps) ).
thf(1260,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Option_Othe @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( c_Predicate_Opred__comp @ B @ B @ B @ c_fequal @ ( c_Predicate_Opred__comp @ B @ B @ B @ A @ c_fequal ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__comp__r) ).
thf(1063,plain,
! [A: $i,B: $i] :
( ( c_Predicate_Opred__comp @ B @ B @ B @ c_fequal @ ( c_Predicate_Opred__comp @ B @ B @ B @ A @ c_fequal ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Ovimage @ A @ E @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI2) ).
thf(538,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)],[62]) ).
thf(241,axiom,
hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Com_Opname ) @ ( c_Map_Odom @ tc_Com_Opname @ tc_Com_Ocom @ c_Com_Obody ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__dom__body) ).
thf(1342,plain,
hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Com_Opname ) @ ( c_Map_Odom @ tc_Com_Opname @ tc_Com_Ocom @ c_Com_Obody ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A )
<=> ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( c_Natural_Oevalc @ C @ B @ E )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I8_J) ).
thf(913,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A )
=> ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( c_Natural_Oevalc @ C @ B @ E )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A ) ) ) ) )
& ( ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( c_Natural_Oevalc @ C @ B @ E )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A ) ) ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(288,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) )
=> ~ ! [B: $i] :
( ( hAPP @ c_Com_Obody @ A )
!= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WTs__elim__cases_I7_J) ).
thf(1507,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) )
=> ~ ! [B: $i] :
( ( hAPP @ c_Com_Obody @ A )
!= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(930,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(1127,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)],[183]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ B ) @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(320,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ B ) @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(116,axiom,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(782,plain,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequivp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp) ).
thf(1441,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequivp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OSemi @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I46_J) ).
thf(885,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OSemi @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCall @ F @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I43_J) ).
thf(1046,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCall @ F @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
thf(1298,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)],[231]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I45_J) ).
thf(719,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Orestrict__map @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Orestrict__map @ E @ D @ C @ A ) ) @ B ) @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__map__insert) ).
thf(372,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Orestrict__map @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Orestrict__map @ E @ D @ C @ A ) ) @ B ) @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Predicate_Oconversep @ E @ D @ ( c_Predicate_Opred__comp @ E @ C @ D @ B @ A ) )
= ( c_Predicate_Opred__comp @ D @ C @ E @ ( c_Predicate_Oconversep @ C @ D @ A ) @ ( c_Predicate_Oconversep @ E @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__pred__comp) ).
thf(587,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Predicate_Oconversep @ E @ D @ ( c_Predicate_Opred__comp @ E @ C @ D @ B @ A ) )
= ( c_Predicate_Opred__comp @ D @ C @ E @ ( c_Predicate_Oconversep @ C @ D @ A ) @ ( c_Predicate_Oconversep @ E @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(1511,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)],[289]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( C != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).
thf(949,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)],[146]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= ( c_Option_Ooption_ONone @ D ) )
=> ( ( c_Map_Omap__comp @ D @ C @ B @ A @ F @ E )
= ( c_Option_Ooption_ONone @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__simps_I1_J) ).
thf(460,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= ( c_Option_Ooption_ONone @ D ) )
=> ( ( c_Map_Omap__comp @ D @ C @ B @ A @ F @ E )
= ( c_Option_Ooption_ONone @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I50_J) ).
thf(902,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ C @ A ) @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OIfTrue) ).
thf(969,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ C @ A ) @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ C @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ~ ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WTs__elim__cases_I5_J) ).
thf(1232,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ C @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ~ ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
thf(1087,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)],[173]) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(1514,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ H @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ C @ B @ A @ H @ E ) @ G ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
thf(1465,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ H @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ C @ B @ A @ H @ E ) @ G ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WTs__elim__cases_I6_J) ).
thf(1334,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
<=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I6_J) ).
thf(834,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(966,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)],[150]) ).
thf(197,axiom,
! [A: $i] :
( ~ ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(1183,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(1151,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)],[190]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( c_Natural_Oevalc @ D @ B @ A ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( c_Natural_Oevalc @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I5_J) ).
thf(937,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( c_Natural_Oevalc @ D @ B @ A ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( c_Natural_Oevalc @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( c_Com_OWT__bodies
=> ( ( ( hAPP @ c_Com_Obody @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT__bodiesD) ).
thf(1383,plain,
! [A: $i,B: $i] :
( c_Com_OWT__bodies
=> ( ( ( hAPP @ c_Com_Obody @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ B @ A ) @ D )
= ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I2_J) ).
thf(1020,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ B @ A ) @ D )
= ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) @ C @ B @ A )
<=> ? [F: $i] :
( ( c_Natural_Oevaln @ E @ C @ B @ F )
& ( c_Natural_Oevaln @ D @ F @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I4_J) ).
thf(774,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) @ C @ B @ A )
=> ? [F: $i] :
( ( c_Natural_Oevaln @ E @ C @ B @ F )
& ( c_Natural_Oevaln @ D @ F @ B @ A ) ) )
& ( ? [F: $i] :
( ( c_Natural_Oevaln @ E @ C @ B @ F )
& ( c_Natural_Oevaln @ D @ F @ B @ A ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__union @ D @ C @ B ) @ A )
= ( c_Lazy__Sequence_Oappend @ D @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__union__def) ).
thf(1394,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)],[252]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequivp @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__symp) ).
thf(1345,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequivp @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A )
<=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I9_J) ).
thf(1405,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A )
=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A ) )
& ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( c_Map_Odom @ C @ B @ ( hAPP @ ( c_Map_Omap__of @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__dom__map__of) ).
thf(507,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( c_Map_Odom @ C @ B @ ( hAPP @ ( c_Map_Omap__of @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(312,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
<=> ( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
| ( ( ( hAPP @ C @ B )
= ( c_Option_Ooption_ONone @ E ) )
& ( ( hAPP @ D @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__Some__iff) ).
thf(396,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
| ( ( ( hAPP @ C @ B )
= ( c_Option_Ooption_ONone @ E ) )
& ( ( hAPP @ D @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ) )
& ( ( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
| ( ( ( hAPP @ C @ B )
= ( c_Option_Ooption_ONone @ E ) )
& ( ( hAPP @ D @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Hilbert__Choice_OEps @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).
thf(1526,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Hilbert__Choice_OEps @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ F @ E @ D @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).
thf(428,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)],[32]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__def) ).
thf(1201,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)],[205]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A )
<=> ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I8_J) ).
thf(1074,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A )
=> ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) ) )
& ( ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_Option_Ooption_ONone @ A ) )
<=> ? [C: $i] :
( B
= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__None__eq) ).
thf(942,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( c_Option_Ooption_ONone @ A ) )
=> ? [C: $i] :
( B
= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) )
& ( ? [C: $i] :
( B
= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
=> ( B
!= ( c_Option_Ooption_ONone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( c_Option_Ooption_ONone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__map__def) ).
thf(529,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( c_Option_Ooption_ONone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__case @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(1438,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)],[263]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( c_FunDef_Oreduction__pair @ B @ ( hAPP @ ( hAPP @ ( c_FunDef_Orp__inv__image @ D @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(1199,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)],[204]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__empty @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__empty @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__empty__def) ).
thf(810,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)],[121]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Map_Omap__add @ F @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ C ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ ( c_Map_Omap__add @ F @ E @ D @ C ) ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__upd) ).
thf(381,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Map_Omap__add @ F @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ C ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ ( c_Map_Omap__add @ F @ E @ D @ C ) ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Map_Omap__le @ D @ C @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ ( tc_Option_Ooption @ C ) ) @ B ) @ A ) @ ( c_Option_Ooption_ONone @ C ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upd__None__map__le) ).
thf(334,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Map_Omap__le @ D @ C @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ ( tc_Option_Ooption @ C ) ) @ B ) @ A ) @ ( c_Option_Ooption_ONone @ C ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__not__random__dseq @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__not__seq @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(1387,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)],[250]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
thf(746,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)],[109]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).
thf(1343,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ D @ A ) @ E @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OIfTrue) ).
thf(952,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ D @ A ) @ E @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevaln @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__Suc) ).
thf(598,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevaln @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oreflp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflpE) ).
thf(1502,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oreflp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( c_Option_Ooption_ONone @ B )
!= ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osimps_I2_J) ).
thf(729,plain,
! [A: $i,B: $i] :
( ( c_Option_Ooption_ONone @ B )
!= ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(219,axiom,
hBOOL @ c_fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(1255,plain,
hBOOL @ c_fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ G ) @ B ) ) @ F ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ F ) @ A ) ) @ G ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
thf(302,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ G ) @ B ) ) @ F ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ F ) @ A ) ) @ G ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ G @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ C ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
thf(467,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)],[43]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A @ B )
<=> ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( c_Natural_Oevaln @ C @ B @ A @ E )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I7_J) ).
thf(625,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A @ B )
=> ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( c_Natural_Oevaln @ C @ B @ A @ E )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( c_Natural_Oevaln @ C @ B @ A @ E )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A @ B ) ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
thf(1178,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)],[196]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__2) ).
thf(1296,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OWhile @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I58_J) ).
thf(889,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OWhile @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep) ).
thf(1027,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)],[161]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Big__Operators_Osemilattice__big @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).
thf(1195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Big__Operators_Osemilattice__big @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) @ B @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OWhileTrue) ).
thf(710,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) @ B @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ B ) @ C @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OWhileFalse) ).
thf(1106,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ B ) @ C @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(852,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)],[127]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] : ( c_Map_Omap__le @ C @ B @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__le__refl) ).
thf(435,plain,
! [A: $i,B: $i,C: $i] : ( c_Map_Omap__le @ C @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I35_J) ).
thf(583,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I41_J) ).
thf(830,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I51_J) ).
thf(874,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCond @ F @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I37_J) ).
thf(650,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCond @ F @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
thf(1328,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)],[238]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oconversep @ C @ B @ ( c_Predicate_Oconversep @ B @ C @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__conversep) ).
thf(1121,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oconversep @ C @ B @ ( c_Predicate_Oconversep @ B @ C @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
thf(499,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)],[52]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ( ( B
= ( c_Hilbert__Choice_OEps @ A @ C ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exE__some) ).
thf(1397,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ( ( B
= ( c_Hilbert__Choice_OEps @ A @ C ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
<=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I5_J) ).
thf(980,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ C ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_OLocal) ).
thf(1498,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ C ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( c_Option_Ooption_ONone @ C ) )
=> ( ( c_Map_Oran @ B @ C @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ B @ ( tc_Option_Ooption @ C ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Map_Oran @ B @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ran__map__upd) ).
thf(339,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( c_Option_Ooption_ONone @ C ) )
=> ( ( c_Map_Oran @ B @ C @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ B @ ( tc_Option_Ooption @ C ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Map_Oran @ B @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ C ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_OIf) ).
thf(1461,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ C ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__le @ E @ D @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A )
=> ( c_Map_Omap__le @ E @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__le__mapE) ).
thf(476,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__le @ E @ D @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A )
=> ( c_Map_Omap__le @ E @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(1446,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OLocal @ F @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I42_J) ).
thf(590,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OLocal @ F @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( c_Option_Oset @ D @ C ) ) )
=> ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( ( C
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ospec) ).
thf(1039,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( c_Option_Oset @ D @ C ) ) )
=> ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( ( C
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ E @ D @ C )
=> ( ( c_Natural_Oevalc @ B @ C @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ E @ B ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OSemi) ).
thf(547,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ E @ D @ C )
=> ( ( c_Natural_Oevalc @ B @ C @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ E @ B ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Opos__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Opos__single @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__single__def) ).
thf(1324,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)],[236]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
<=> ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).
thf(1263,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) ) )
& ( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
thf(1456,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WTs__elim__cases_I8_J) ).
thf(1192,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).
thf(911,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)],[139]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ B ) @ A ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(1246,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ B ) @ A ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OCond @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I54_J) ).
thf(503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OCond @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__empty @ B ) @ A )
= ( c_Lazy__Sequence_Oempty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
thf(1451,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)],[268]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ C @ B @ A )
<=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eval__eq) ).
thf(738,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Natural_Oevalc @ C @ B @ A )
=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) )
& ( ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A )
=> ( c_Natural_Oevalc @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(1131,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ A @ C ) @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OIfFalse) ).
thf(654,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ A @ C ) @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ D @ C @ B )
=> ( ( c_Natural_Oevalc @ D @ C @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com__det) ).
thf(1060,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ D @ C @ B )
=> ( ( c_Natural_Oevalc @ D @ C @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
<=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I5_J) ).
thf(1050,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_Oequations_I6_J) ).
thf(1241,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) )
& ( ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Oinject) ).
thf(633,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ C ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_OCall) ).
thf(1187,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ C ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__1) ).
thf(1185,plain,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevalc @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__evalc) ).
thf(926,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevalc @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__insert) ).
thf(906,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)],[138]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( c_Natural_Oevaln @ E @ C @ B @ A ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I5_J) ).
thf(750,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( c_Natural_Oevaln @ E @ C @ B @ A ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ B @ A @ E ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(1251,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ B @ A @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__le @ D @ C @ B @ A )
=> ( ( c_Map_Omap__le @ D @ C @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__le__antisym) ).
thf(425,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__le @ D @ C @ B @ A )
=> ( ( c_Map_Omap__le @ D @ C @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ B ) @ A ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
thf(1483,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ B ) @ A ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ E ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
<=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__code) ).
thf(1273,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Option_Oset @ C @ A ) ) )
<=> ( A
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_elem__set) ).
thf(689,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Option_Oset @ C @ A ) ) )
=> ( A
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) ) )
& ( ( A
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Option_Oset @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(1278,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)],[226]) ).
thf(1,conjecture,
hBOOL @ ( hAPP @ c_Com_OWT @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( hAPP @ c_Com_OWT @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(298,plain,
~ ( hBOOL @ ( hAPP @ c_Com_OWT @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I39_J) ).
thf(513,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__le @ E @ D @ C @ B )
=> ( ( c_Map_Omap__le @ E @ D @ A @ B )
=> ( ( c_Map_Omap__le @ E @ D @ C @ ( c_Map_Omap__add @ E @ D @ C @ A ) )
=> ( c_Map_Omap__le @ E @ D @ ( c_Map_Omap__add @ E @ D @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__le__mapI) ).
thf(430,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__le @ E @ D @ C @ B )
=> ( ( c_Map_Omap__le @ E @ D @ A @ B )
=> ( ( c_Map_Omap__le @ E @ D @ C @ ( c_Map_Omap__add @ E @ D @ C @ A ) )
=> ( c_Map_Omap__le @ E @ D @ ( c_Map_Omap__add @ E @ D @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ ( tc_Option_Ooption @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ C ) ) @ B ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) ) ) @ D )
= ( hAPP @ ( c_Set_Oimage @ F @ ( tc_Option_Ooption @ C ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__map__upd) ).
thf(375,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ ( tc_Option_Ooption @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ C ) ) @ B ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) ) ) @ D )
= ( hAPP @ ( c_Set_Oimage @ F @ ( tc_Option_Ooption @ C ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__wfPD) ).
thf(733,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)],[105]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ D ) @ ( c_Map_Odom @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_domI) ).
thf(743,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ D ) @ ( c_Map_Odom @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_OSemi) ).
thf(1403,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(1520,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequivp @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__transp) ).
thf(1124,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequivp @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ G @ F @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ E @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(1256,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)],[220]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_Oequations_I5_J) ).
thf(1226,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_New__Random__Sequence_Oneg__union @ F @ E @ D @ C @ B @ A )
= ( c_New__DSequence_Oneg__union @ F @ ( hAPP @ ( hAPP @ ( hAPP @ E @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__union__def) ).
thf(1488,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_New__Random__Sequence_Oneg__union @ F @ E @ D @ C @ B @ A )
= ( c_New__DSequence_Oneg__union @ F @ ( hAPP @ ( hAPP @ ( hAPP @ E @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ G @ F )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ D ) )
=> ( ( c_Map_Omap__comp @ E @ C @ B @ A @ G @ F )
= ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__simps_I2_J) ).
thf(391,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ G @ F )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ D ) )
=> ( ( c_Map_Omap__comp @ E @ C @ B @ A @ G @ F )
= ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I53_J) ).
thf(572,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
thf(1371,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)],[247]) ).
thf(233,axiom,
~ ( hBOOL @ c_fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(1312,plain,
~ ( hBOOL @ c_fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Com_Ocom_OCond @ F @ E @ D )
= ( c_Com_Ocom_OCond @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I4_J) ).
thf(611,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Com_Ocom_OCond @ F @ E @ D )
= ( c_Com_Ocom_OCond @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( c_Com_Ocom_OCond @ F @ E @ D )
= ( c_Com_Ocom_OCond @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( ( c_Com_Ocom_OBODY @ B )
= ( c_Com_Ocom_OBODY @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).
thf(1090,plain,
! [A: $i,B: $i] :
( ( ( ( c_Com_Ocom_OBODY @ B )
= ( c_Com_Ocom_OBODY @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Com_Ocom_OBODY @ B )
= ( c_Com_Ocom_OBODY @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__2) ).
thf(1224,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ C ) ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) )
<=> ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( hAPP @ E @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upd__Some__unfold) ).
thf(350,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ C ) ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) )
=> ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( hAPP @ E @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ) )
& ( ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( hAPP @ E @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ C ) ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I49_J) ).
thf(540,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I61_J) ).
thf(604,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_Map_Odom @ F @ D @ C ) ) )
=> ( ( c_Map_Omap__add @ F @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ D ) ) @ B ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Omap__add @ F @ D @ B @ C ) ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__upd__left) ).
thf(419,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_Map_Odom @ F @ D @ C ) ) )
=> ( ( c_Map_Omap__add @ F @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ D ) ) @ B ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Omap__add @ F @ D @ B @ C ) ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OWhile @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I47_J) ).
thf(509,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OWhile @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(1376,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)],[248]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).
thf(863,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(990,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)],[155]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(996,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)],[156]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A )
= ( c_Option_Ooption_ONone @ D ) )
<=> ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ D ) )
& ( ( hAPP @ C @ A )
= ( c_Option_Ooption_ONone @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__None) ).
thf(451,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A )
= ( c_Option_Ooption_ONone @ D ) )
=> ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ D ) )
& ( ( hAPP @ C @ A )
= ( c_Option_Ooption_ONone @ D ) ) ) )
& ( ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ D ) )
& ( ( hAPP @ C @ A )
= ( c_Option_Ooption_ONone @ D ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A )
= ( c_Option_Ooption_ONone @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__if) ).
thf(567,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)],[71]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( C
= ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(387,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)],[23]) ).
thf(276,axiom,
hBOOL @ ( hAPP @ c_Com_OWT @ v_c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(1471,plain,
hBOOL @ ( hAPP @ c_Com_OWT @ v_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Com_Ocom_OCall @ F @ E @ D )
= ( c_Com_Ocom_OCall @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I7_J) ).
thf(816,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Com_Ocom_OCall @ F @ E @ D )
= ( c_Com_Ocom_OCall @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( c_Com_Ocom_OCall @ F @ E @ D )
= ( c_Com_Ocom_OCall @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ B ) @ A )
= C )
<=> ( ( hAPP @ C @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(323,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ B ) @ A )
= C )
=> ( ( hAPP @ C @ B )
= A ) )
& ( ( ( hAPP @ C @ B )
= A )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ B ) @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I59_J) ).
thf(594,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( c_Option_Ooption_ONone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__out) ).
thf(726,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( c_Option_Ooption_ONone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
thf(895,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)],[135]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ C ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ B ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) )
=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upd__eqD1) ).
thf(330,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ C ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ B ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(203,axiom,
class_HOL_Oequal @ tc_Com_Ocom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com__Ocom__HOL_Oequal) ).
thf(1198,plain,
class_HOL_Oequal @ tc_Com_Ocom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(1474,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)],[278]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Oneg__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Ohb__single @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
thf(1213,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)],[208]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ A @ D ) @ E @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OIfFalse) ).
thf(780,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ A @ D ) @ E @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(131,axiom,
! [A: $i] : ( c_Equiv__Relations_Oequivp @ A @ c_fequal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_identity__equivp) ).
thf(883,plain,
! [A: $i] : ( c_Equiv__Relations_Oequivp @ A @ c_fequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(608,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)],[82]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(394,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)],[25]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( c_Hilbert__Choice_OEps @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
thf(1113,plain,
! [A: $i,B: $i] :
( ( c_Hilbert__Choice_OEps @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ A ) @ ( hAPP @ B @ A ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(299,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ A ) @ ( hAPP @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I34_J) ).
thf(1102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Map_Odom @ D @ B @ A ) ) )
=> ? [E: $i] :
( ( hAPP @ A @ C )
= ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_domD) ).
thf(521,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Map_Odom @ D @ B @ A ) ) )
=> ? [E: $i] :
( ( hAPP @ A @ C )
= ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(194,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( c_Divides_Odivmod__nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).
thf(1171,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( c_Divides_Odivmod__nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCall @ F @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I57_J) ).
thf(1066,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCall @ F @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oequivp @ B @ A )
<=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
<=> ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__def) ).
thf(1528,plain,
! [A: $i,B: $i] :
( ( ( c_Equiv__Relations_Oequivp @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
=> ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) )
& ( ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
=> ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) )
& ( ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ) )
=> ( c_Equiv__Relations_Oequivp @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_New__DSequence_Oneg__map @ E @ D @ C @ B @ A )
= ( c_Lazy__Sequence_Ohb__map @ E @ D @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__map__def) ).
thf(1208,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_New__DSequence_Oneg__map @ E @ D @ C @ B @ A )
= ( c_Lazy__Sequence_Ohb__map @ E @ D @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hAPP @ C @ ( hAPP @ D @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(1467,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)],[275]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) )
<=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex) ).
thf(1145,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_New__DSequence_Oneg__union @ D @ C @ B ) @ A )
= ( c_Lazy__Sequence_Oappend @ ( tc_Option_Ooption @ D ) @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__union__def) ).
thf(553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_New__DSequence_Oneg__union @ D @ C @ B ) @ A )
= ( c_Lazy__Sequence_Oappend @ ( tc_Option_Ooption @ D ) @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
| ( ( ( hAPP @ C @ B )
= ( c_Option_Ooption_ONone @ E ) )
& ( ( hAPP @ D @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__SomeD) ).
thf(490,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
| ( ( ( hAPP @ C @ B )
= ( c_Option_Ooption_ONone @ E ) )
& ( ( hAPP @ D @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Com_Ocom_OLocal @ F @ E @ D )
= ( c_Com_Ocom_OLocal @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I2_J) ).
thf(675,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Com_Ocom_OLocal @ F @ E @ D )
= ( c_Com_Ocom_OLocal @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( c_Com_Ocom_OLocal @ F @ E @ D )
= ( c_Com_Ocom_OLocal @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(185,axiom,
! [A: $i] :
( ( ( hAPP @ c_Com_Obody @ A )
!= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_OBody) ).
thf(1134,plain,
! [A: $i] :
( ( ( hAPP @ c_Com_Obody @ A )
!= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).
thf(648,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)],[88]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(342,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) )
| ~ ( hBOOL @ B )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__3) ).
thf(1472,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) )
| ~ ( hBOOL @ B )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I44_J) ).
thf(525,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
<=> ( B
= ( c_Option_Ooption_ONone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Some__eq) ).
thf(712,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
=> ( B
= ( c_Option_Ooption_ONone @ A ) ) )
& ( ( B
= ( c_Option_Ooption_ONone @ A ) )
=> ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I62_J) ).
thf(640,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OLocal @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I40_J) ).
thf(1070,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OLocal @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
thf(705,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)],[97]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Map_Oran @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ranI) ).
thf(707,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Map_Oran @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) @ B @ A )
<=> ? [E: $i] :
( ( c_Natural_Oevalc @ D @ B @ E )
& ( c_Natural_Oevalc @ C @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I4_J) ).
thf(971,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) @ B @ A )
=> ? [E: $i] :
( ( c_Natural_Oevalc @ D @ B @ E )
& ( c_Natural_Oevalc @ C @ E @ A ) ) )
& ( ? [E: $i] :
( ( c_Natural_Oevalc @ D @ B @ E )
& ( c_Natural_Oevalc @ C @ E @ A ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).
thf(954,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)],[148]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A )
!= ( c_Option_Ooption_ONone @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osimps_I3_J) ).
thf(1098,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A )
!= ( c_Option_Ooption_ONone @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ G @ F @ E @ D @ C ) @ B ) @ A ) )
<=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ H ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ H ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
thf(1432,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ G @ F @ E @ D @ C ) @ B ) @ A ) )
=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ H ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ H ) @ A ) ) ) )
& ( ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ H ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ H ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ G @ F @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Map_Omap__le @ F @ E @ D @ C )
=> ( c_Map_Omap__le @ F @ E @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__le__upd) ).
thf(370,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Map_Omap__le @ F @ E @ D @ C )
=> ( c_Map_Omap__le @ F @ E @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(41,axiom,
! [A: $i] :
( ( class_Enum_Oenum @ A )
=> ( class_Enum_Oenum @ ( tc_Option_Ooption @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Enum_Oenum) ).
thf(463,plain,
! [A: $i] :
( ( class_Enum_Oenum @ A )
=> ( class_Enum_Oenum @ ( tc_Option_Ooption @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(64,axiom,
! [A: $i] :
( ( c_Predicate_Oconversep @ A @ A @ c_fequal )
= c_fequal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__eq) ).
thf(544,plain,
! [A: $i] :
( ( c_Predicate_Oconversep @ A @ A @ c_fequal )
= c_fequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(44,axiom,
! [A: $i] : ( class_HOL_Oequal @ ( tc_Option_Ooption @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__HOL_Oequal) ).
thf(470,plain,
! [A: $i] : ( class_HOL_Oequal @ ( tc_Option_Ooption @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(576,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)],[73]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ C @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).
thf(1285,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ C @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_Oequations_I4_J) ).
thf(1218,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(1358,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)],[246]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ D ) @ C ) @ B ) ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
thf(336,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ D ) @ C ) @ B ) ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ C @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_Oequations_I3_J) ).
thf(1427,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) )
& ( ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
thf(1140,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)],[187]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Map_Omap__comp @ F @ E @ D @ C @ B @ A )
= ( c_Option_Ooption_ONone @ E ) )
<=> ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ F ) )
| ? [G: $i] :
( ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ G ) )
& ( ( hAPP @ C @ G )
= ( c_Option_Ooption_ONone @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__None__iff) ).
thf(1008,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Map_Omap__comp @ F @ E @ D @ C @ B @ A )
= ( c_Option_Ooption_ONone @ E ) )
=> ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ F ) )
| ? [G: $i] :
( ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ G ) )
& ( ( hAPP @ C @ G )
= ( c_Option_Ooption_ONone @ E ) ) ) ) )
& ( ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ F ) )
| ? [G: $i] :
( ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ G ) )
& ( ( hAPP @ C @ G )
= ( c_Option_Ooption_ONone @ E ) ) ) )
=> ( ( c_Map_Omap__comp @ F @ E @ D @ C @ B @ A )
= ( c_Option_Ooption_ONone @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Com_Ocom_OSemi @ D @ C )
= ( c_Com_Ocom_OSemi @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).
thf(656,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Com_Ocom_OSemi @ D @ C )
= ( c_Com_Ocom_OSemi @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Com_Ocom_OSemi @ D @ C )
= ( c_Com_Ocom_OSemi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I60_J) ).
thf(1023,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__code) ).
thf(1353,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)],[245]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I52_J) ).
thf(600,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
thf(465,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)],[42]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OBody) ).
thf(1459,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCond @ F @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I56_J) ).
thf(556,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCond @ F @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
thf(1553,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
thf(482,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)],[49]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).
thf(671,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)],[93]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WTs__elim__cases_I3_J) ).
thf(1517,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ B @ A @ E ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(1216,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ B @ A @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).
thf(1390,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)],[251]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(771,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)],[113]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__eq) ).
thf(1108,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)],[178]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
<=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exists__code) ).
thf(1448,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Oneg__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Oneg__single @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__single__def) ).
thf(1189,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)],[200]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Map_Omap__le @ F @ E @ D @ C )
=> ( c_Map_Omap__le @ F @ E @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ D ) @ B ) @ ( c_Option_Ooption_ONone @ E ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ C ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__le__imp__upd__le) ).
thf(368,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Map_Omap__le @ F @ E @ D @ C )
=> ( c_Map_Omap__le @ F @ E @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ D ) @ B ) @ ( c_Option_Ooption_ONone @ E ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ C ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ A @ A )
<=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( c_Natural_Oevalc @ B @ A @ D )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I7_J) ).
thf(844,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ A @ A )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( c_Natural_Oevalc @ B @ A @ D )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ D @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( c_Natural_Oevalc @ B @ A @ D )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ D @ A ) ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(225,axiom,
( c_Com_Obody
= ( hAPP @ ( c_Map_Omap__of @ tc_Com_Opname @ tc_Com_Ocom ) @ c_Com_Obodies ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_body__def) ).
thf(1276,plain,
( c_Com_Obody
= ( hAPP @ ( c_Map_Omap__of @ tc_Com_Opname @ tc_Com_Ocom ) @ c_Com_Obodies ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_While) ).
thf(1253,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I55_J) ).
thf(517,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(1481,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)],[279]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__single @ C @ B ) @ A )
= ( hAPP @ ( c_Lazy__Sequence_Osingle @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
thf(1523,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)],[293]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I38_J) ).
thf(786,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_OwfP @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
thf(961,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)],[149]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(813,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)],[122]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ A @ ( tc_Option_Ooption @ C ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upd__triv) ).
thf(378,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ A @ ( tc_Option_Ooption @ C ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ C @ A @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(478,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)],[48]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( c_Map_Odom @ A @ C @ E ) )
= ( c_Map_Odom @ A @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__dom) ).
thf(899,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( c_Map_Odom @ A @ C @ E ) )
= ( c_Map_Odom @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
thf(536,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)],[61]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold) ).
thf(1030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ B @ A )
=> ~ ! [E: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ E ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I6_J) ).
thf(1491,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ B @ A )
=> ~ ! [E: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ E ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OSemi @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I48_J) ).
thf(667,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OSemi @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(1294,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OCall @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I63_J) ).
thf(549,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OCall @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) )
| ( hBOOL @ B )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__3) ).
thf(1444,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) )
| ( hBOOL @ B )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(192,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) )
<=> ? [B: $i] :
( ( hAPP @ c_Com_Obody @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_Oequations_I7_J) ).
thf(1161,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) )
=> ? [B: $i] :
( ( hAPP @ c_Com_Obody @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ B ) ) )
& ( ? [B: $i] :
( ( hAPP @ c_Com_Obody @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ B ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(800,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)],[119]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ A ) @ D ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
thf(1116,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)],[180]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
thf(1348,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)],[244]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__in) ).
thf(432,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(1546,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)],[296]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) @ A ) )
<=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
thf(1303,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)],[232]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__rec @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(1148,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)],[189]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
thf(735,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)],[106]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).
thf(422,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)],[30]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
<=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I6_J) ).
thf(790,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ A @ B ) @ D )
= ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I3_J) ).
thf(564,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ A @ B ) @ D )
= ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ B @ A ) @ E ) @ D ) @ C )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(305,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ B @ A ) @ E ) @ D ) @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
thf(1314,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)],[234]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversepD) ).
thf(1495,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageD) ).
thf(807,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)],[120]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ B @ D @ A @ F ) @ E )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__find__right) ).
thf(437,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ B @ D @ A @ F ) @ E )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
<=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(696,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)],[96]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Map_Omap__le @ D @ C @ B @ ( c_Map_Omap__add @ D @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__le__map__add) ).
thf(474,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Map_Omap__le @ D @ C @ B @ ( c_Map_Omap__add @ D @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(1410,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)],[257]) ).
thf(163,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(1033,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
thf(1288,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)],[228]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ B @ C @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OWhileTrue) ).
thf(928,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ B @ C @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Oran @ C @ E @ ( c_Map_Orestrict__map @ C @ E @ B @ A ) ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( ( hAPP @ B @ F )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ran__restrictD) ).
thf(415,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Oran @ C @ E @ ( c_Map_Orestrict__map @ C @ E @ B @ A ) ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( ( hAPP @ B @ F )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ C @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_Oequations_I8_J) ).
thf(1236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__iff) ).
thf(1268,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ E ) @ ( hAPP @ ( c_Set_Ovimage @ A @ C @ F ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI) ).
thf(644,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)],[87]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).
thf(1505,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__1) ).
thf(1500,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ A @ B ) @ D )
= ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I1_J) ).
thf(723,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ A @ B ) @ D )
= ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1320,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Map_Odom @ D @ B @ A ) ) )
<=> ( ( hAPP @ A @ C )
!= ( c_Option_Ooption_ONone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_domIff) ).
thf(755,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Map_Odom @ D @ B @ A ) ) )
=> ( ( hAPP @ A @ C )
!= ( c_Option_Ooption_ONone @ B ) ) )
& ( ( ( hAPP @ A @ C )
!= ( c_Option_Ooption_ONone @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Map_Odom @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__add @ E @ D @ C @ ( c_Map_Omap__add @ E @ D @ B @ A ) )
= ( c_Map_Omap__add @ E @ D @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__assoc) ).
thf(496,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__add @ E @ D @ C @ ( c_Map_Omap__add @ E @ D @ B @ A ) )
= ( c_Map_Omap__add @ E @ D @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
<=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(1417,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)],[258]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A )
=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I6_J) ).
thf(1463,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A )
=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ F @ E @ D @ C )
=> ( ( c_Natural_Oevaln @ B @ C @ D @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ F @ B ) @ E @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OSemi) ).
thf(1037,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ F @ E @ D @ C )
=> ( ( c_Natural_Oevaln @ B @ C @ D @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ F @ B ) @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OLocal @ F @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I36_J) ).
thf(560,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OLocal @ F @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1559,plain,
$false,
inference(e,[status(thm)],[1337,1168,1454,893,1211,1005,1401,1422,449,1173,408,977,1158,582,762,878,440,1426,384,1137,472,1327,1260,1063,538,1342,913,1507,930,1127,320,782,1441,885,1046,1298,719,372,587,1511,949,460,902,969,1232,1087,1514,1465,1334,834,966,1183,1151,937,1383,1020,774,1394,1345,1405,507,312,396,1526,428,1201,1074,942,529,1438,1199,810,381,334,1387,746,1343,952,598,1502,729,1255,302,467,625,1178,1296,889,1027,1195,710,1106,852,435,583,830,874,650,1328,1121,499,1397,980,1498,339,1461,476,1446,590,1039,547,1324,1263,1456,1192,911,1246,503,1451,738,1131,654,1060,1050,1241,633,1187,1185,926,906,750,1251,425,1483,1273,689,1278,298,513,430,375,733,743,1403,1520,1124,1256,1226,1488,391,572,1371,1312,611,1090,1224,350,540,604,419,509,1376,863,990,996,451,567,387,1471,816,323,594,726,895,330,1198,1474,1213,780,883,608,394,1113,299,1102,521,1171,1066,1528,1208,1467,1145,553,490,675,1134,648,342,1472,525,712,640,1070,705,707,971,954,1098,1432,370,463,544,470,576,1285,1218,1358,336,1427,1140,1008,656,1023,1353,600,465,1459,556,1553,482,671,1517,1216,1390,771,1108,1448,1189,368,844,1276,1253,517,1481,1523,786,961,813,378,478,899,536,1030,1491,667,1294,549,1444,1161,800,1116,1348,432,1546,1303,1148,735,422,790,564,305,1314,1495,807,437,696,474,1410,1033,1288,928,415,1236,1268,644,1505,1500,723,1320,755,496,1417,309,1463,1037,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW374+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 22:30:18 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.99/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.98/1.45 % [INFO] Parsing done (569ms).
% 2.98/1.46 % [INFO] Running in sequential loop mode.
% 3.23/1.67 % [INFO] eprover registered as external prover.
% 3.23/1.67 % [INFO] cvc4 registered as external prover.
% 3.23/1.67 % [INFO] Scanning for conjecture ...
% 5.01/2.12 % [INFO] Found a conjecture and 5248 axioms. Running axiom selection ...
% 6.49/2.68 % [INFO] Axiom selection finished. Selected 295 axioms (removed 4953 axioms).
% 6.98/2.90 % [INFO] Problem is first-order (TPTP FOF).
% 7.24/2.92 % [INFO] Type checking passed.
% 7.24/2.92 % [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 ...
% 16.49/5.13 % External prover 'e' found a proof!
% 16.49/5.13 % [INFO] Killing All external provers ...
% 16.49/5.13 % Time passed: 4586ms (effective reasoning time: 3662ms)
% 16.49/5.13 % 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)>
% 16.49/5.13 % Axioms used in derivation (295): fact_While, fact_map__add__le__mapE, fact_divmod__nat__rel__divmod__nat, fact_evalc_Oequations_I8_J, fact_New__DSequence_Oneg__map__def, fact_com__det, fact_map__upd__Some__unfold, fact_com_Osimps_I56_J, fact_insertCI, fact_pos__union__def, fact_restrict__map__def, fact_accp_Oequations, fact_finite__dom__map__of, fact_image__insert, fact_ran__restrictD, fact_map__add__dom__app__simps_I3_J, fact_evalc_OIfFalse, fact_evaln__elim__cases_I5_J, fact_upd__None__map__le, fact_conversep_Oequations, fact_folding__image__simple__idem_Oin__idem, fact_map__add__SomeD, fact_insert__iff, fact_map__add__Some__iff, fact_com_Osimps_I50_J, fact_divmod__nat__eq, fact_prod_Orecs, fact_equivp__transp, fact_com_Osimps_I37_J, fact_insertI1, fact_WT_Oequations_I5_J, fact_pair__box_Oinject, fact_com_Osimps_I40_J, fact_WTs__elim__cases_I3_J, fact_comm__monoid__big_Oinfinite, fact_folding__image__simple_Oeq__fold__g, fact_option_Osimps_I2_J, fact_com_Osimps_I46_J, fact_com_Osimps_I2_J, fact_WTs__elim__cases_I8_J, help_c__fconj__3, fact_com_Osimps_I60_J, help_c__fequal__2, conj_3, fact_divmod__nat__rel__unique, fact_map__add__upd, fact_neg__single__def, fact_com_Osimps_I59_J, fact_evalc__elim__cases_I6_J, help_c__fFalse__1, fact_evaln__Suc, fact_type__definition_OAbs__inject, fact_com_Osimps_I62_J, fact_split__paired__All, fact_restrict__map__insert, fact_map__le__trans, fact_map__add__dom__app__simps_I2_J, fact_fold__graph__imp__finite, fact_WT_OLocal, arity_Option__Ooption__Nat_Osize, fact_conversep_Ointros, fact_folding__one__idem_Oin__idem, fact_fun__upd__same, fact_folding__image__simple__idem_Oinsert__idem, fact_com_Osimps_I55_J, fact_someI__ex, fact_com_Osimps_I53_J, fact_nat_Oinject, fact_option_Osimps_I3_J, fact_domI, fact_com_Osimps_I5_J, fact_folding__one_Oeq__fold, fact_ord_OatMost__iff, fact_folding__one_Oeq__fold_H, fact_folding__one__idem_Oeq__fold__idem_H, fact_com_Osimps_I3_J, fact_rev__image__eqI, fact_vimage__eq, fact_elem__set, fact_map__add__upd__left, fact_restrict__out, fact_ord_OgreaterThan__iff, fact_WT__bodiesD, fact_Powp__def, fact_fun__upd__idem, fact_pos__empty__def, fact_Rep__Integ__inject, fact_reflpE, help_c__fconj__2, fact_evalc_OIfTrue, arity_Option__Ooption__HOL_Oequal, fact_neg__union__def, fact_domD, fact_com_Osimps_I41_J, fact_WT_OSemi, fact_ran__map__upd, help_c__fNot__1, fact_map__le__iff__map__add__commute, fact_evalc_Oequations_I4_J, fact_WT_Oequations_I7_J, fact_insert__code, fact_evaln_OBody, fact_fun__upd__other, fact_com_Osimps_I57_J, fact_evaln_OWhileFalse, fact_evaln_Oequations_I7_J, fact_type__definition_ORep, fact_com_Osimps_I63_J, fact_New__DSequence_Oneg__single__def, fact_com_Osimps_I35_J, fact_com_Osimps_I47_J, fact_insert__image, conj_2, fact_evaln_OSemi, fact_vimageI2, fact_eq__mem, fact_evaln_OIfTrue, fact_some__eq__ex, fact_finite__insert, fact_equivp__symp, fact_insert__absorb2, fact_insertI2, fact_folding__one__idem_Oidem, fact_com_Osimps_I7_J, fact_insert__absorb, fact_fun__upd__apply, fact_evalc_OSemi, fact_eqset__imp__iff, fact_vimageI, fact_WTs__elim__cases_I4_J, fact_body__def, fact_com_Osimps_I45_J, fact_map__le__antisym, fact_wfP__accp__iff, fact_pos__single__def, help_c__fdisj__1, fact_map__add__le__mapI, help_c__fimplies__1, fact_accp__wfPD, fact_finite__dom__body, fact_WT_OBody, fact_folding__image__simple_Oinsert, help_c__fequal__1, fact_finite__imageI, fact_vimage__code, fact_rp__inv__image__rp, fact_insert__commute, fact_fun__upd__triv, fact_pair__box_Orecs, fact_pred__comp_Ointros, fact_equivp__def, fact_not__Some__eq, fact_DomainP_Ointros, fact_WT_Oequations_I3_J, fact_map__le__def, fact_accp__downward, fact_fun__upd__idem__iff, fact_com_Osimps_I6_J, fact_map__upd__triv, fact_WT_Oequations_I4_J, fact_evalc_Oequations_I9_J, fact_converse__pred__comp, fact_eq__comp__r, help_c__fconj__1, fact_ord_OlessThan__iff, fact_Pair__inject, fact_card__insert__if, help_c__fdisj__2, fact_domIff, fact_not__None__eq, fact_map__le__map__add, arity_Option__Ooption__Enum_Oenum, fact_fold__graph_OinsertI, fact_evaln_OIfFalse, fact_Suc__inject, fact_conversep__iff, fact_ext, help_c__fNot__2, fact_enum__all, fact_com_Osimps_I42_J, fact_com_Osimps_I54_J, fact_RangeP_Ointros, fact_map__upd__eqD1, fact_semilattice__big_OF__eq, fact_ospec, fact_equivp__reflp, fact_someI, fact_com_Osimps_I48_J, fact_fun__upd__upd, fact_map__comp__None__iff, fact_n__not__Suc__n, fact_evaln_Oequations_I5_J, fact_WTs__elim__cases_I6_J, fact_restrict__in, fact_com_Osimps_I34_J, fact_insert__ident, fact_com_Osimps_I38_J, fact_WT_Oequations_I8_J, fact_WT_OCall, fact_conversep__eq, fact_evaln_Oequations_I6_J, fact_evalc_OBody, fact_map__le__refl, fact_com_Osimps_I36_J, fact_WTs__elim__cases_I5_J, fact_evalc_OWhileFalse, fact_map__comp__simps_I1_J, fact_map__comp__simps_I2_J, fact_card__insert__disjoint, fact_ord_OgreaterThanLessThan__iff, fact_eq__mem__trans, fact_ord_OatLeastLessThan__iff, help_c__fimplies__2, fact_evalc_OWhileTrue, fact_RangeP_Oequations, fact_map__le__upd, fact_New__DSequence_Opos__empty__def, fact_accp_Osimps, arity_Com__Ocom__HOL_Oequal, fact_map__add__dom__app__simps_I1_J, conj_1, fact_pred__comp_Oequations, fact_comm__monoid__big_OF__eq, fact_tfl__some, fact_com_Osimps_I44_J, fact_enum__ex, fact_evaln_OWhileTrue, fact_map__comp__Some__iff, fact_evalc_Oequations_I5_J, fact_evaln__elim__cases_I6_J, fact_com_Osimps_I39_J, fact_image__iff, fact_Pair__eq, fact_map__add__assoc, arity_Com__Ocom__Nat_Osize, fact_evalc__elim__cases_I5_J, fact_ord_OgreaterThanAtMost__iff, fact_fun__upd__def, fact_all__code, fact_equalityCE, fact_option_Oinject, fact_finite_OinsertI, fact_fun__upd__twist, fact_conversep__conversep, fact_insert__dom, fact_com_Osimps_I58_J, fact_image__map__upd, help_c__fimplies__3, fact_type__definition_OAbs__inverse, fact_image__eqI, fact_ranI, fact_evaln_Oequations_I4_J, help_c__fTrue__1, fact_exists__code, fact_com_Osimps_I61_J, fact_insertE, fact_evaln_Oequations_I9_J, fact_map__add__find__right, fact_WT_OIf, fact_New__DSequence_Opos__single__def, fact_conversepD, fact_some__sym__eq__trivial, fact_type__definition_ORep__inject, fact_exE__some, fact_com_Osimps_I49_J, fact_com_Osimps_I43_J, fact_eqelem__imp__iff, fact_pair__box_Osimps_I2_J, fact_com_Osimps_I52_J, fact_Suc__n__not__n, fact_pos__not__random__dseq__def, fact_DomainP_Oequations, fact_ord_OatLeastAtMost__iff, fact_New__DSequence_Opos__union__def, fact_the_Osimps, fact_evalc_Oequations_I6_J, fact_evaln_Oequations_I8_J, fact_map__le__imp__upd__le, fact_mem__def, fact_WT_Oequations_I6_J, fact_vimageD, fact_type__definition_ORep__inverse, fact_identity__equivp, fact_New__DSequence_Oneg__union__def, fact_WTs__elim__cases_I7_J, fact_com_Osimps_I4_J, fact_map__add__None, fact_folding__image__simple__idem_Oidem, fact_evalc_Oequations_I7_J, fact_com_Osimps_I51_J, fact_eval__eq, help_c__fdisj__3, fact_evaln__evalc, fact_ord_OatLeast__iff, fact_imageI
% 16.49/5.13 % No. of inferences in proof: 594
% 16.49/5.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4586 ms resp. 3662 ms w/o parsing
% 17.34/5.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.34/5.27 % [INFO] Killing All external provers ...
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