TSTP Solution File: SCT123+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT123+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:50:38 EDT 2023
% Result : Theorem 24.76s 6.95s
% Output : Refutation 25.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 614
% Syntax : Number of formulae : 1145 ( 284 unt; 85 typ; 0 def)
% Number of atoms : 2856 ( 832 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 33168 ( 293 ~; 41 |; 247 &;31079 @)
% ( 103 <=>;1405 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 190 ( 190 >; 0 *; 0 +; 0 <<)
% Number of symbols : 87 ( 85 usr; 9 con; 0-6 aty)
% Number of variables : 4449 ( 0 ^;4410 !; 39 ?;4449 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_member_type,type,
c_member: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(v_L_type,type,
v_L: $i ).
thf(c_Arrow__Order__Mirabelle_OProf_type,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Predicate_Oconversep_type,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Relation_OId__on_type,type,
c_Relation_OId__on: $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(c_Relation_Osingle__valued_type,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_Relation_Orefl__on_type,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(class_Orderings_Otop_type,type,
class_Orderings_Otop: $i > $o ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(class_Lattices_Osemilattice__inf_type,type,
class_Lattices_Osemilattice__inf: $i > $o ).
thf(c_Lattices_Osemilattice__inf__class_Oinf_type,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(c_Equiv__Relations_Oequiv_type,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_Equiv__Relations_Ocongruent2_type,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Equiv__Relations_Ocongruent_type,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(c_FuncSet_Oextensional_type,type,
c_FuncSet_Oextensional: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Nitpick_Ofold__graph_H_type,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Recdef_Oadm__wf_type,type,
c_Recdef_Oadm__wf: $i > $i > $i > $i > $o ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Arrow__Order__Mirabelle_Obelow_type,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
thf(c_Wellfounded_Oacyclic_type,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(class_Lattices_Obounded__lattice__top_type,type,
class_Lattices_Obounded__lattice__top: $i > $o ).
thf(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: $i > $i > $i > $o ).
thf(c_Wellfounded_Oacc_type,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_fNot_type,type,
c_fNot: $i ).
thf(c_FuncSet_OPi_type,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(class_Groups_Ominus_type,type,
class_Groups_Ominus: $i > $o ).
thf(c_Recdef_Ocut_type,type,
c_Recdef_Ocut: $i > $i > $i ).
thf(c_COMBI_type,type,
c_COMBI: $i > $i ).
thf(c_Predicate_Oinv__imagep_type,type,
c_Predicate_Oinv__imagep: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_Omkbot_type,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(c_FuncSet_Oextensional__funcset_type,type,
c_FuncSet_Oextensional__funcset: $i > $i > $i > $i > $i ).
thf(c_HOL_Oundefined_type,type,
c_HOL_Oundefined: $i > $i ).
thf(c_Arrow__Order__Mirabelle_Odictator_type,type,
c_Arrow__Order__Mirabelle_Odictator: $i > $i > $o ).
thf(c_FuncSet_Ocompose_type,type,
c_FuncSet_Ocompose: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Predicate_ODomainP_type,type,
c_Predicate_ODomainP: $i > $i > $i > $i > $o ).
thf(class_Lattices_Obounded__lattice__bot_type,type,
class_Lattices_Obounded__lattice__bot: $i > $o ).
thf(c_FuncSet_Orestrict_type,type,
c_FuncSet_Orestrict: $i > $i > $i > $i > $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_Recdef_Osame__fst_type,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(c_Relation_Oirrefl_type,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Equiv__Relations_Oquotient_type,type,
c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Oabove_type,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(c_Relation_Ototal__on_type,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(c_Wellfounded_Olex__prod_type,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OIIA_type,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
thf(c_Predicate_ORangeP_type,type,
c_Predicate_ORangeP: $i > $i > $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_Ounanimity_type,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(c_Relation_Oinv__image_type,type,
c_Relation_Oinv__image: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_type,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_Nitpick_Orefl_H_type,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_FunDef_Oin__rel_type,type,
c_FunDef_Oin__rel: $i > $i > $i > $i > $i > $o ).
thf(c_Set_Othe__elem_type,type,
c_Set_Othe__elem: $i > $i > $i ).
thf(97,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(892,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__inf @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__mono) ).
thf(1823,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__inf @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Ototal__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) )
<=> ( c_Relation_Ototal__on @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__converse) ).
thf(2336,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Ototal__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) )
=> ( c_Relation_Ototal__on @ C @ B @ A ) )
& ( ( c_Relation_Ototal__on @ C @ B @ A )
=> ( c_Relation_Ototal__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__iff) ).
thf(1767,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).
thf(1899,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__UN__eq2) ).
thf(1315,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
thf(941,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
thf(1554,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__fun__def) ).
thf(1168,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Relation_OId__on @ D @ A ) ) )
<=> ( ( C = B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__iff) ).
thf(2306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Relation_OId__on @ D @ A ) ) )
=> ( ( C = B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Relation_OId__on @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(478,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mktop__Lin) ).
thf(2341,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__leI) ).
thf(2412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) @ ( hAPP @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ORange @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Relation_ORange @ E @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__insert) ).
thf(1237,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ORange @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Relation_ORange @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__E) ).
thf(777,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
thf(555,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__insert__distrib) ).
thf(1818,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_Oextensional__funcset @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ B ) ) @ ( c_COMBK @ B @ C @ ( c_HOL_Oundefined @ B ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__empty__domain) ).
thf(1295,plain,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_Oextensional__funcset @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ B ) ) @ ( c_COMBK @ B @ C @ ( c_HOL_Oundefined @ B ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
thf(1211,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__apply) ).
thf(2512,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(289,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(1596,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)],[289]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ B ) @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__nondisjoint) ).
thf(1290,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ B ) @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(408,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(2062,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).
thf(2014,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).
thf(2099,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntI) ).
thf(1443,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(348,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(1808,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)],[348]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__empty__left) ).
thf(994,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__iff) ).
thf(2527,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(878,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singletonE) ).
thf(655,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_FunDef_Oin__rel @ E @ D @ C @ B @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(2380,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_FunDef_Oin__rel @ E @ D @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) )
=> ( c_FunDef_Oin__rel @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Oaccp @ C @ B @ A )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( c_Wellfounded_Oaccp @ C @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(1971,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Wellfounded_Oaccp @ C @ B @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( c_Wellfounded_Oaccp @ C @ B @ D ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( c_Wellfounded_Oaccp @ C @ B @ D ) )
=> ( c_Wellfounded_Oaccp @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Recdef_Oadm__wf @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ C ) ) @ ( c_COMBS @ D @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ C ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ C ) @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) ) @ ( c_Recdef_Ocut @ D @ C ) ) @ B ) ) ) ) @ ( c_COMBI @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__lemma) ).
thf(1533,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Recdef_Oadm__wf @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ C ) ) @ ( c_COMBS @ D @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ C ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ C ) @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) ) @ ( c_Recdef_Ocut @ D @ C ) ) @ B ) ) ) ) @ ( c_COMBI @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ ( c_FuncSet_OPi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ c_Arrow__Order__Mirabelle_OProf @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ C ) ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_Odictator @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictatorI) ).
thf(1078,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ ( c_FuncSet_OPi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ c_Arrow__Order__Mirabelle_OProf @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ C ) ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_Odictator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffE) ).
thf(1671,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot2E) ).
thf(1756,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__empty) ).
thf(1735,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ B ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ A ) ) @ D ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedD) ).
thf(1999,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ B ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ A ) ) @ D ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(60,axiom,
class_Lattices_Olattice @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
thf(715,plain,
class_Lattices_Olattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int2) ).
thf(1275,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseI) ).
thf(1327,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ C ) ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(1342,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ C ) ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb1) ).
thf(1954,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ ( hAPP @ ( c_Relation_Oconverse @ E @ F ) @ D ) )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Relation_OImage @ E @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ B ) @ ( c_Relation_OImage @ E @ F @ D ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__INT__eq) ).
thf(2434,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ ( hAPP @ ( c_Relation_Oconverse @ E @ F ) @ D ) )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Relation_OImage @ E @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ B ) @ ( c_Relation_OImage @ E @ F @ D ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Ofun__upd @ D @ C @ B @ A @ ( hAPP @ B @ A ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(1872,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Ofun__upd @ D @ C @ B @ A @ ( hAPP @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Ocongruent @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ B ) @ A ) ) @ D ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruentD) ).
thf(2168,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Ocongruent @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ B ) @ A ) ) @ D ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( hAPP @ A @ E ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( c_HOL_Oundefined @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__def) ).
thf(1260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( hAPP @ A @ E ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( c_HOL_Oundefined @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Equiv__Relations_Oequiv @ J @ I @ H )
=> ( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_Equiv__Relations_Ocongruent2 @ J @ G @ ( tc_fun @ D @ tc_HOL_Obool ) @ H @ E @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ J ) @ B ) @ I ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ F ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ J @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ J @ J @ H ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ J ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ J @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ J ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ G @ G @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class2) ).
thf(930,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Equiv__Relations_Oequiv @ J @ I @ H )
=> ( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_Equiv__Relations_Ocongruent2 @ J @ G @ ( tc_fun @ D @ tc_HOL_Obool ) @ H @ E @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ J ) @ B ) @ I ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ F ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ J @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ J @ J @ H ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ J ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ J @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ J ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ G @ G @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(2360,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ K @ J ) ) @ I ) @ ( c_FuncSet_OPi @ K @ J @ H @ ( c_COMBK @ ( tc_fun @ J @ tc_HOL_Obool ) @ K @ G ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ J @ F ) ) @ E ) @ ( c_FuncSet_OPi @ J @ F @ G @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ J @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ B ) @ ( c_FuncSet_OPi @ F @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ F @ A ) ) ) )
=> ( ( c_FuncSet_Ocompose @ K @ F @ C @ H @ B @ ( c_FuncSet_Ocompose @ K @ J @ F @ H @ E @ I ) )
= ( c_FuncSet_Ocompose @ K @ J @ C @ H @ ( c_FuncSet_Ocompose @ J @ F @ C @ G @ B @ E ) @ I ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__assoc) ).
thf(1095,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ K @ J ) ) @ I ) @ ( c_FuncSet_OPi @ K @ J @ H @ ( c_COMBK @ ( tc_fun @ J @ tc_HOL_Obool ) @ K @ G ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ J @ F ) ) @ E ) @ ( c_FuncSet_OPi @ J @ F @ G @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ J @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ B ) @ ( c_FuncSet_OPi @ F @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ F @ A ) ) ) )
=> ( ( c_FuncSet_Ocompose @ K @ F @ C @ H @ B @ ( c_FuncSet_Ocompose @ K @ J @ F @ H @ E @ I ) )
= ( c_FuncSet_Ocompose @ K @ J @ C @ H @ ( c_FuncSet_Ocompose @ J @ F @ C @ G @ B @ E ) @ I ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ ( c_FuncSet_Orestrict @ E @ C @ B @ D ) ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrictI) ).
thf(2216,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ ( c_FuncSet_Orestrict @ E @ C @ B @ D ) ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Wellfounded_Oacc @ C @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__subset) ).
thf(2348,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Wellfounded_Oacc @ C @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I1_J) ).
thf(1576,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Diff) ).
thf(709,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
<=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__iff) ).
thf(841,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) )
& ( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
thf(885,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) )
=> ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(1650,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I5_J) ).
thf(1359,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__constant) ).
thf(1724,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__INT__eq2) ).
thf(1803,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(1904,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__iff) ).
thf(1887,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__I) ).
thf(651,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(165,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_L ) @ c_Arrow__Order__Mirabelle_OLin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(1127,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_L ) @ c_Arrow__Order__Mirabelle_OLin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I4_J) ).
thf(1782,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__absorb) ).
thf(1287,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(570,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) @ C ) @ ( c_Relation_Oconverse @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__UNION) ).
thf(1430,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) @ C ) @ ( c_Relation_Oconverse @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I3_J) ).
thf(719,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ C @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) ) @ c_fequal ) ) @ B ) @ A ) )
<=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__noteq) ).
thf(1907,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ C @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) ) @ c_fequal ) ) @ B ) @ A ) )
=> ( B != A ) )
& ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ C @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) ) @ c_fequal ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) ) )
<=> ( ( B != A )
& ( ( B = D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__above) ).
thf(2444,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) ) )
=> ( ( B != A )
& ( ( B = D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) )
& ( ( ( B != A )
& ( ( B = D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__inf__iff) ).
thf(1323,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(253,axiom,
class_Orderings_Opreorder @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(1455,plain,
class_Orderings_Opreorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(356,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
<=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IIA__def) ).
thf(1832,plain,
! [A: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ A )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) ) ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_OIIA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(1132,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__D) ).
thf(1055,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__assoc) ).
thf(1409,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNION__empty__conv_I2_J) ).
thf(1660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(209,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(1298,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)],[209]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD1) ).
thf(2274,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I2_J) ).
thf(917,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD1) ).
thf(1545,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
thf(853,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ ( c_FuncSet_Ocompose @ F @ D @ E @ C @ B @ A ) ) @ ( c_FuncSet_Oextensional @ F @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__extensional) ).
thf(1479,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ ( c_FuncSet_Ocompose @ F @ D @ E @ C @ B @ A ) ) @ ( c_FuncSet_Oextensional @ F @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) )
=> ( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class__iff) ).
thf(1347,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) )
=> ( ( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
thf(770,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(1741,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ E ) @ B ) @ A ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ D @ ( hAPP @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__INF__iff) ).
thf(1115,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ E ) @ B ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ D @ ( hAPP @ A @ F ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ D @ ( hAPP @ A @ F ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ D @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_FuncSet_Ocompose @ E @ D @ D @ B @ ( c_FuncSet_Orestrict @ D @ D @ ( c_COMBI @ D ) @ A ) @ C )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__compose) ).
thf(1568,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_FuncSet_Ocompose @ E @ D @ D @ B @ ( c_FuncSet_Orestrict @ D @ D @ ( c_COMBI @ D ) @ A ) @ C )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).
thf(2158,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb2) ).
thf(1641,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ G ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ G ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct) ).
thf(1362,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ G ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ G ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OImage @ C @ C @ ( c_Relation_OId__on @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Id__on) ).
thf(1875,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OImage @ C @ C @ ( c_Relation_OId__on @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( c_Set_Othe__elem @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__elem__eq) ).
thf(2533,plain,
! [A: $i,B: $i] :
( ( c_Set_Othe__elem @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(376,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(1922,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)],[376]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ B ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
thf(902,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ B ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ A ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
thf(1704,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ A ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__greatest) ).
thf(870,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseI) ).
thf(1415,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1714,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__UN__flatten) ).
thf(1040,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(449,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(2236,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)],[449]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ODomain @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Relation_ODomain @ E @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__insert) ).
thf(646,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ODomain @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Relation_ODomain @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(1978,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(413,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
thf(2073,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP1__iff) ).
thf(2017,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(2291,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D2) ).
thf(1020,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(15,axiom,
! [A: $i,B: $i] : ( c_Relation_Osingle__valued @ B @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
thf(574,plain,
! [A: $i,B: $i] : ( c_Relation_Osingle__valued @ B @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower2) ).
thf(2281,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( ( hAPP @ D @ C )
!= ( hAPP @ D @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ D ) @ ( c_FuncSet_Oextensional__funcset @ F @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ C ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ ( c_Fun_Ofun__upd @ F @ B @ D @ C @ ( c_HOL_Oundefined @ B ) ) ) @ ( c_FuncSet_Oextensional__funcset @ F @ B @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ ( hAPP @ D @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__fun__upd__restricts__rangeI) ).
thf(1119,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( ( hAPP @ D @ C )
!= ( hAPP @ D @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ D ) @ ( c_FuncSet_Oextensional__funcset @ F @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ C ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ ( c_Fun_Ofun__upd @ F @ B @ D @ C @ ( c_HOL_Oundefined @ B ) ) ) @ ( c_FuncSet_Oextensional__funcset @ F @ B @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ ( hAPP @ D @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(2002,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ ( c_Relation_Oinv__image @ C @ F @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ E ) ) @ ( hAPP @ A @ D ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__inv__image) ).
thf(2286,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ ( c_Relation_Oinv__image @ C @ F @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ E ) ) @ ( hAPP @ A @ D ) ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ E ) ) @ ( hAPP @ A @ D ) ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ ( c_Relation_Oinv__image @ C @ F @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ORange @ B @ D @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeE) ).
thf(1433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ORange @ B @ D @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNION__empty__conv_I1_J) ).
thf(1201,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( c_Nitpick_Orefl_H @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
thf(2367,plain,
! [A: $i,B: $i] :
( ( ( c_Nitpick_Orefl_H @ B @ A )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) )
=> ( c_Nitpick_Orefl_H @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
thf(2437,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I9_J) ).
thf(1896,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( c_HOL_Oundefined @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__apply) ).
thf(2190,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( c_HOL_Oundefined @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) )
=> ( ( ( c_Equiv__Relations_Oquotient @ E @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C )
= ( c_Equiv__Relations_Oquotient @ E @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class__iff2) ).
thf(1447,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) )
=> ( ( ( ( c_Equiv__Relations_Oquotient @ E @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C )
= ( c_Equiv__Relations_Oquotient @ E @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( ( c_Equiv__Relations_Oquotient @ E @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C )
= ( c_Equiv__Relations_Oquotient @ E @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
thf(956,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left) ).
thf(1796,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ F @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__UN) ).
thf(1072,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ F @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD2) ).
thf(1697,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__iff) ).
thf(1242,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(360,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__I) ).
thf(1863,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__Diff) ).
thf(1604,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(546,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
thf(925,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(2118,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I7_J) ).
thf(2047,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseD) ).
thf(2232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(2083,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Predicate_ORangeP @ D @ C @ B @ A )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) )
=> ( c_Predicate_ORangeP @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(375,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(1915,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)],[375]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__eq) ).
thf(1708,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
thf(2093,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__commute) ).
thf(798,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
thf(1057,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD2) ).
thf(1163,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= A ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I1_J) ).
thf(2589,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= A ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__UNIV) ).
thf(2409,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(98,axiom,
! [A: $i] :
( ~ ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(894,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb1) ).
thf(825,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(524,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) ) )
<=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mktop) ).
thf(2541,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) ) )
=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) ) )
& ( ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int__distrib) ).
thf(1355,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2E) ).
thf(1123,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(1676,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__E) ).
thf(1751,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
thf(1487,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(1883,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_Oextensional__funcset @ F @ E @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__mem) ).
thf(1217,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_Oextensional__funcset @ F @ E @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(598,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__subset) ).
thf(693,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( c_Relation_OImage @ D @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__eq__UN) ).
thf(630,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( c_Relation_OImage @ D @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
thf(2414,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I4_J) ).
thf(729,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(103,axiom,
class_Groups_Ominus @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
thf(916,plain,
class_Groups_Ominus @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(291,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 @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ C ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ ( c_Fun_Ofun__upd @ D @ G @ C @ A @ F ) ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__extend__domainI) ).
thf(1602,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 @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ C ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ ( c_Fun_Ofun__upd @ D @ G @ C @ A @ F ) ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infE) ).
thf(1968,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(1178,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int__distrib2) ).
thf(1951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
thf(583,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ F ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__I) ).
thf(1787,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ F ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(480,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(2345,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)],[480]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__equiv__class) ).
thf(1407,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ A ) @ B ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ D ) @ C ) @ ( c_COMBK @ D @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__const) ).
thf(1634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ D ) @ C ) @ ( c_COMBK @ D @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
thf(1573,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downward) ).
thf(2068,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
thf(1624,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ D @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
=> ( C = A ) )
& ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
thf(2327,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( c_Relation_Oinv__image @ C @ D @ B @ A ) )
= ( c_Relation_Oinv__image @ C @ D @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__inv__image) ).
thf(2213,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( c_Relation_Oinv__image @ C @ D @ B @ A ) )
= ( c_Relation_Oinv__image @ C @ D @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I4_J) ).
thf(2492,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
thf(551,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__mem) ).
thf(1128,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
thf(1402,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(451,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(2245,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(1983,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UNIV__left) ).
thf(2115,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ A ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ B ) )
=> ( ( hAPP @ C @ F )
= ( hAPP @ A @ F ) ) )
=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensionalityI) ).
thf(1270,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ A ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ B ) )
=> ( ( hAPP @ C @ F )
= ( hAPP @ A @ F ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ C ) @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2I) ).
thf(948,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ C ) @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ C ) ) @ ( c_FuncSet_Orestrict @ D @ C @ B @ A ) ) @ ( c_FuncSet_Oextensional @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__extensional) ).
thf(1794,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ C ) ) @ ( c_FuncSet_Orestrict @ D @ C @ B @ A ) ) @ ( c_FuncSet_Oextensional @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oirrefl @ B @ A )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__def) ).
thf(1375,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oirrefl @ B @ A )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) )
=> ( c_Relation_Oirrefl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oidem) ).
thf(1856,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(286,axiom,
! [A: $i,B: $i] : ( c_Relation_Ototal__on @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__empty) ).
thf(1587,plain,
! [A: $i,B: $i] : ( c_Relation_Ototal__on @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUPR__apply) ).
thf(2509,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI) ).
thf(1878,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__singleton) ).
thf(1138,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclD) ).
thf(2268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__rtrancl) ).
thf(1397,plain,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) )
<=> ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ C ) )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
thf(742,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) )
=> ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ C ) )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) ) )
& ( ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ C ) )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) )
=> ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(578,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
thf(697,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(154,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(1089,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)],[154]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ImageE) ).
thf(1234,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__idem) ).
thf(1762,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(515,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).
thf(2515,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
<=> ( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__eq__iff) ).
thf(1683,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) ) )
& ( ( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(216,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__iff) ).
thf(1329,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__mono) ).
thf(2323,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Equiv__Relations_Ocongruent2 @ J @ I @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ J @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ J @ J ) @ D ) @ C ) ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ I @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ I @ I ) @ B ) @ A ) ) @ F ) )
=> ( ( hAPP @ ( hAPP @ E @ D ) @ B )
= ( hAPP @ ( hAPP @ E @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2D) ).
thf(1461,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Equiv__Relations_Ocongruent2 @ J @ I @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ J @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ J @ J ) @ D ) @ C ) ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ I @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ I @ I ) @ B ) @ A ) ) @ F ) )
=> ( ( hAPP @ ( hAPP @ E @ D ) @ B )
= ( hAPP @ ( hAPP @ E @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Oabove @ A @ C @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_above__Lin) ).
thf(1584,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Oabove @ A @ C @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
thf(1937,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards) ).
thf(1810,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ ( c_FuncSet_Orestrict @ E @ C @ B @ D ) ) @ ( c_FuncSet_OPi @ E @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__in__funcset) ).
thf(1214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ ( c_FuncSet_Orestrict @ E @ C @ B @ D ) ) @ ( c_FuncSet_OPi @ E @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__idemp) ).
thf(1644,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD2) ).
thf(679,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Relation_OId__on @ B @ A ) )
= ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Id__on) ).
thf(2317,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Relation_OId__on @ B @ A ) )
= ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
<=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__in__conv) ).
thf(1419,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).
thf(1028,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(399,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__top @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__top__right) ).
thf(2023,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__top @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ C ) ) @ B ) @ ( c_FuncSet_Oextensional @ D @ C @ A ) ) )
=> ( ( c_FuncSet_Orestrict @ D @ C @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__restrict) ).
thf(1292,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ C ) ) @ B ) @ ( c_FuncSet_Oextensional @ D @ C @ A ) ) )
=> ( ( c_FuncSet_Orestrict @ D @ C @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I_H) ).
thf(933,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_Equiv__Relations_Oequiv @ E @ A @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class) ).
thf(686,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_Equiv__Relations_Oequiv @ E @ A @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__commute) ).
thf(1075,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equals0D) ).
thf(837,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(355,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(1825,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)],[355]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mem) ).
thf(997,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Oacyclic @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B )
=> ( c_Wellfounded_Oacyclic @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__subset) ).
thf(2519,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Oacyclic @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B )
=> ( c_Wellfounded_Oacyclic @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
thf(2536,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greatest) ).
thf(2304,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D2) ).
thf(2566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ORange @ B @ D @ A ) ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__iff) ).
thf(1002,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ORange @ B @ D @ A ) ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ORange @ B @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_FuncSet_Ocompose @ E @ E @ D @ B @ C @ ( c_FuncSet_Orestrict @ E @ E @ ( c_COMBI @ E ) @ B ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__Id) ).
thf(1599,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_FuncSet_Ocompose @ E @ E @ D @ B @ C @ ( c_FuncSet_Orestrict @ E @ E @ ( c_COMBI @ E ) @ B ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Recdef_Oadm__wf @ D @ C @ B @ A )
<=> ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ H ) @ G ) ) @ B ) )
=> ( ( hAPP @ E @ H )
= ( hAPP @ F @ H ) ) )
=> ( ( hAPP @ ( hAPP @ A @ E ) @ G )
= ( hAPP @ ( hAPP @ A @ F ) @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__wf__def) ).
thf(779,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Recdef_Oadm__wf @ D @ C @ B @ A )
=> ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ H ) @ G ) ) @ B ) )
=> ( ( hAPP @ E @ H )
= ( hAPP @ F @ H ) ) )
=> ( ( hAPP @ ( hAPP @ A @ E ) @ G )
= ( hAPP @ ( hAPP @ A @ F ) @ G ) ) ) )
& ( ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ H ) @ G ) ) @ B ) )
=> ( ( hAPP @ E @ H )
= ( hAPP @ F @ H ) ) )
=> ( ( hAPP @ ( hAPP @ A @ E ) @ G )
= ( hAPP @ ( hAPP @ A @ F ) @ G ) ) )
=> ( c_Recdef_Oadm__wf @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntE) ).
thf(1530,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(1539,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(254,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(1456,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)],[254]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).
thf(1382,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D1) ).
thf(2387,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
thf(1231,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Oaccp @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( c_Wellfounded_Oaccp @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(1552,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Oaccp @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( c_Wellfounded_Oaccp @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( c_Predicate_ORangeP @ B @ A @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(2243,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( c_Predicate_ORangeP @ B @ A @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ ( c_Transitive__Closure_Ortrancl @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
thf(1060,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ ( c_Transitive__Closure_Ortrancl @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ B ) @ ( c_FuncSet_Oextensional__funcset @ F @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ E ) @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ ( c_HOL_Oundefined @ C ) ) ) @ ( c_FuncSet_Oextensional__funcset @ F @ C @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__restrict__domain) ).
thf(1050,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ B ) @ ( c_FuncSet_Oextensional__funcset @ F @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ E ) @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ ( c_HOL_Oundefined @ C ) ) ) @ ( c_FuncSet_Oextensional__funcset @ F @ C @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
thf(605,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ODomain @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= ( c_Relation_ORange @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__converse) ).
thf(1759,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ODomain @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= ( c_Relation_ORange @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UNIV__right) ).
thf(633,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(313,axiom,
! [A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__empty) ).
thf(1695,plain,
! [A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
thf(1563,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B = A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(558,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( B = A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__diff__def) ).
thf(1732,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__not__insert) ).
thf(1814,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).
thf(1086,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ B @ F ) @ ( hAPP @ A @ F ) ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__INTER) ).
thf(953,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ B @ F ) @ ( hAPP @ A @ F ) ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_FuncSet_Oextensional__funcset @ B @ A @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__empty__range) ).
thf(1185,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_FuncSet_Oextensional__funcset @ B @ A @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(20,axiom,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ A @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
thf(586,plain,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ A @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ C @ A )
= ( c_HOL_Oundefined @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__arb) ).
thf(1996,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ C @ A )
= ( c_HOL_Oundefined @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Osingle__valued @ C @ B @ A )
<=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ F ) ) @ A ) )
=> ( E = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__def) ).
thf(2423,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Osingle__valued @ C @ B @ A )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ F ) ) @ A ) )
=> ( E = F ) ) ) )
& ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ F ) ) @ A ) )
=> ( E = F ) ) )
=> ( c_Relation_Osingle__valued @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__mono) ).
thf(662,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INFI__apply) ).
thf(2121,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__left) ).
thf(1135,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
thf(965,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id__on) ).
thf(618,plain,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ A ) @ C ) @ B ) )
<=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ G ) @ B ) ) @ C ) )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cuts__eq) ).
thf(2176,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ A ) @ C ) @ B ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ G ) @ B ) ) @ C ) )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) ) )
& ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ G ) @ B ) ) @ C ) )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__converse__eq) ).
thf(1103,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ G ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__I) ).
thf(1219,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ G ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
<=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
thf(2028,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) )
& ( ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( c_Fun_Ofun__upd @ B @ A @ E @ D @ C )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(689,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( c_Fun_Ofun__upd @ B @ A @ E @ D @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ A )
= ( c_Relation_ODomain @ B @ C @ ( hAPP @ ( c_Relation_Oconverse @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__def) ).
thf(2524,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ A )
= ( c_Relation_ODomain @ B @ C @ ( hAPP @ ( c_Relation_Oconverse @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_ODomain @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
thf(1278,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Relation_ODomain @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) )
=> ( ( c_Relation_ODomain @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(373,axiom,
class_Orderings_Obot @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
thf(1906,plain,
class_Orderings_Obot @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
thf(1146,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).
thf(1754,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
thf(2260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(601,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converse) ).
thf(904,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) @ C ) @ ( c_Relation_Oconverse @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__INTER) ).
thf(1007,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) @ C ) @ ( c_Relation_Oconverse @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(294,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(1615,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)],[294]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( c_Predicate_ODomainP @ B @ A @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(2188,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( c_Predicate_ODomainP @ B @ A @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__diff) ).
thf(2489,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).
thf(875,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).
thf(1535,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff1) ).
thf(958,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I5_J) ).
thf(2398,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcsetI) ).
thf(1965,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE) ).
thf(641,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I9_J) ).
thf(936,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Oaccp @ C @ B @ A )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( c_Wellfounded_Oaccp @ C @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(1865,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Wellfounded_Oaccp @ C @ B @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( c_Wellfounded_Oaccp @ C @ B @ D ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( c_Wellfounded_Oaccp @ C @ B @ D ) )
=> ( c_Wellfounded_Oaccp @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
thf(1332,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
thf(1092,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( class_Orderings_Obot @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
thf(1765,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( class_Orderings_Obot @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(804,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(57,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(704,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)],[57]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_ORange @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__empty__iff) ).
thf(1464,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Relation_ORange @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) )
=> ( ( c_Relation_ORange @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__if) ).
thf(1224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(5,axiom,
! [A: $i] :
( ( c_Predicate_Oconversep @ A @ A @ c_fequal )
= c_fequal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__eq) ).
thf(540,plain,
! [A: $i] :
( ( c_Predicate_Oconversep @ A @ A @ c_fequal )
= c_fequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
thf(672,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( c_FuncSet_Oextensional @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ B @ A ) ) @ ( c_COMBK @ A @ B @ ( c_HOL_Oundefined @ A ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__empty) ).
thf(2521,plain,
! [A: $i,B: $i] :
( ( c_FuncSet_Oextensional @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ B @ A ) ) @ ( c_COMBK @ A @ B @ ( c_HOL_Oundefined @ A ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(446,axiom,
! [A: $i] :
( ( c_Relation_OId__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__empty) ).
thf(2229,plain,
! [A: $i] :
( ( c_Relation_OId__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseD) ).
thf(1894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__insert) ).
thf(1542,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ G @ B ) @ F @ A )
= ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ F @ A ) @ G @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
thf(567,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ G @ B ) @ F @ A )
= ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ F @ A ) @ G @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
thf(1144,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I9_J) ).
thf(737,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).
thf(1690,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Int) ).
thf(1571,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C )
<=> ( ( hAPP @ C @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(863,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C )
=> ( ( hAPP @ C @ B )
= A ) )
& ( ( ( hAPP @ C @ B )
= A )
=> ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__triv) ).
thf(681,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(523,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(2538,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ F ) @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ D ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UN__distrib2) ).
thf(2257,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ F ) @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ D ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(287,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(1589,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_Oconversep @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Predicate_Oconversep @ D @ C @ B ) ) @ ( c_Predicate_Oconversep @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__meet) ).
thf(1492,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_Oconversep @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Predicate_Oconversep @ D @ C @ B ) ) @ ( c_Predicate_Oconversep @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(466,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__def) ).
thf(2299,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I9_J) ).
thf(880,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le1) ).
thf(649,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
thf(1043,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
<=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
thf(2197,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) )
& ( ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
thf(1307,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI1) ).
thf(890,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
<=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__converse) ).
thf(1471,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) )
& ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ B @ A ) ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__iff) ).
thf(858,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ B @ A ) ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(353,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(1821,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)],[353]) ).
thf(31,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(621,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)],[31]) ).
thf(84,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(848,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)],[84]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__E) ).
thf(1344,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
thf(2278,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(758,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) )
=> ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hAPP @ ( c_FuncSet_Ocompose @ G @ D @ C @ E @ B @ A ) @ F )
= ( hAPP @ B @ ( hAPP @ A @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__eq) ).
thf(1339,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hAPP @ ( c_FuncSet_Ocompose @ G @ D @ C @ E @ B @ A ) @ F )
= ( hAPP @ B @ ( hAPP @ A @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__commute) ).
thf(2314,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(429,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_Odictator @ B @ A )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictator__def) ).
thf(2129,plain,
! [A: $i,B: $i] :
( ( ( c_Arrow__Order__Mirabelle_Odictator @ B @ A )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) )
=> ( c_Arrow__Order__Mirabelle_Odictator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).
thf(2343,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ODomain @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__domain) ).
thf(609,plain,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ODomain @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( hAPP @ ( c_Relation_OImage @ E @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ E @ F @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__INT__subset) ).
thf(2111,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( hAPP @ ( c_Relation_OImage @ E @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ E @ F @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ B ) @ A )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ B @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__le__iff) ).
thf(1630,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ B ) @ A )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ B @ F ) @ A ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ B @ F ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__empty) ).
thf(1993,plain,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__subset) ).
thf(1556,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(69,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(769,plain,
class_Orderings_Oord @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= ( c_Relation_ODomain @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__converse) ).
thf(943,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= ( c_Relation_ODomain @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_COMBK @ D @ C @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(2252,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_COMBK @ D @ C @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__iff) ).
thf(1171,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ D ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ F ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct) ).
thf(2439,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ D ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ F ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Obounded__lattice__top @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ C ) )
<=> ( ( B
= ( c_Orderings_Otop__class_Otop @ C ) )
& ( A
= ( c_Orderings_Otop__class_Otop @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__eq__top__iff) ).
thf(1926,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Obounded__lattice__top @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ C ) )
=> ( ( B
= ( c_Orderings_Otop__class_Otop @ C ) )
& ( A
= ( c_Orderings_Otop__class_Otop @ C ) ) ) )
& ( ( ( B
= ( c_Orderings_Otop__class_Otop @ C ) )
& ( A
= ( c_Orderings_Otop__class_Otop @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__iff) ).
thf(2350,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) )
=> ( ! [I: $i,J: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ! [K: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
thf(2171,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) )
=> ( ! [I: $i,J: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ! [K: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD1) ).
thf(883,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(180,axiom,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__rtrancl) ).
thf(1176,plain,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(161,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 @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ C ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ ( c_Fun_Ofun__upd @ D @ G @ C @ A @ F ) ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__fun__upd__extends__rangeI) ).
thf(1113,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 @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ C ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ ( c_Fun_Ofun__upd @ D @ G @ C @ A @ F ) ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
thf(1477,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).
thf(2101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( c_Relation_ODomain @ E @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainI) ).
thf(653,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( c_Relation_ODomain @ E @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I) ).
thf(2506,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I5_J) ).
thf(2401,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(315,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(1699,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)],[315]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
thf(636,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(54,axiom,
? [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linear__alt) ).
thf(695,plain,
? [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb2) ).
thf(1066,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice @ B )
=> ( class_Lattices_Obounded__lattice__top @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).
thf(1445,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice @ B )
=> ( class_Lattices_Obounded__lattice__top @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(409,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__inf @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
thf(2064,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__inf @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FuncSet_Oextensional__funcset @ D @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) @ ( c_FuncSet_OPi @ D @ C @ B @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D @ A ) ) ) @ ( c_FuncSet_Oextensional @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__def) ).
thf(1015,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FuncSet_Oextensional__funcset @ D @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) @ ( c_FuncSet_OPi @ D @ C @ B @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D @ A ) ) ) @ ( c_FuncSet_Oextensional @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I1_J) ).
thf(2390,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__acc__down) ).
thf(1250,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UN__distrib) ).
thf(2005,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ A ) ) )
=> ~ ! [E: $i,F: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ F ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ D ) @ E ) @ F ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseE) ).
thf(675,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ A ) ) )
=> ~ ! [E: $i,F: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ F ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ D ) @ E ) @ F ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1,conjecture,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( c_COMBK @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ v_L ) ) @ c_Arrow__Order__Mirabelle_OProf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( c_COMBK @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ v_L ) ) @ c_Arrow__Order__Mirabelle_OProf ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(531,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( c_COMBK @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ v_L ) ) @ c_Arrow__Order__Mirabelle_OProf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Ofun__upd @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ C @ B ) @ C @ A )
= ( c_Fun_Ofun__upd @ F @ E @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
thf(548,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Ofun__upd @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ C @ B ) @ C @ A )
= ( c_Fun_Ofun__upd @ F @ E @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( hAPP @ A @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__apply) ).
thf(927,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( hAPP @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_OPi @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__empty) ).
thf(2503,plain,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_OPi @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Oacyclic @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
<=> ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__insert) ).
thf(812,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Oacyclic @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
=> ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) )
& ( ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
=> ( c_Wellfounded_Oacyclic @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(110,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ B ) ) @ ( c_COMBI @ B ) ) @ ( c_FuncSet_OPi @ B @ B @ A @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__id) ).
thf(939,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ B ) ) @ ( c_COMBI @ B ) ) @ ( c_FuncSet_OPi @ B @ B @ A @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_Osimps) ).
thf(1958,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(553,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ A ) @ D ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).
thf(2124,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ A ) @ D ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ A ) @ D ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__subset) ).
thf(2234,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_Oextensional__funcset @ F @ E @ C @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ D @ A )
= ( c_HOL_Oundefined @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__arb) ).
thf(2333,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_Oextensional__funcset @ F @ E @ C @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ D @ A )
= ( c_HOL_Oundefined @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffI) ).
thf(1018,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
thf(712,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__assoc) ).
thf(1025,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__empty) ).
thf(872,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( ( hAPP @ D @ G )
= ( hAPP @ C @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ D ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ C ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__cong) ).
thf(1156,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( ( hAPP @ D @ G )
= ( hAPP @ C @ G ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ D ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ C ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ C ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ D ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(431,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
<=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unanimity__def) ).
thf(2143,plain,
! [A: $i] :
( ( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ B ) ) ) ) ) )
& ( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ B ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_Ounanimity @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ B ) )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__right) ).
thf(1647,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ B ) )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__not__empty) ).
thf(1368,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__subset) ).
thf(1780,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).
thf(1484,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I5_J) ).
thf(1098,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__empty2) ).
thf(1547,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).
thf(1748,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(580,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__top @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ ( c_Orderings_Otop__class_Otop @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__top__left) ).
thf(855,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__top @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ ( c_Orderings_Otop__class_Otop @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__D) ).
thf(1743,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD) ).
thf(1400,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP1__I) ).
thf(2407,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__cancel) ).
thf(1267,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__commute) ).
thf(1711,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Ototal__on @ C @ B @ A )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ E ) ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ E ) @ D ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__def) ).
thf(2569,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Ototal__on @ C @ B @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ E ) ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ E ) @ D ) ) @ A ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ E ) ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ E ) @ D ) ) @ A ) ) ) ) ) )
=> ( c_Relation_Ototal__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ ( hAPP @ A @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__subset__iff) ).
thf(791,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ ( hAPP @ A @ F ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ ( hAPP @ A @ F ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(183,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(1188,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)],[183]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__D) ).
thf(1785,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( c_Equiv__Relations_Ocongruent @ F @ ( tc_fun @ C @ tc_HOL_Obool ) @ D @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ E ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) @ B )
= ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class) ).
thf(1901,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( c_Equiv__Relations_Ocongruent @ F @ ( tc_fun @ C @ tc_HOL_Obool ) @ D @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ E ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) @ B )
= ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__least) ).
thf(576,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__inject) ).
thf(1679,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(167,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
thf(1130,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_FuncSet_OPi @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) )
<=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__eq__empty) ).
thf(907,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_FuncSet_OPi @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( c_FuncSet_OPi @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(1790,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(321,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__in__Lin) ).
thf(1716,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__empty) ).
thf(1452,plain,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ B ) @ tc_HOL_Obool ) @ ( c_FuncSet_OPi @ E @ B @ C @ A ) @ ( c_FuncSet_OPi @ E @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
thf(1637,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ B ) @ tc_HOL_Obool ) @ ( c_FuncSet_OPi @ E @ B @ C @ A ) @ ( c_FuncSet_OPi @ E @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__mono) ).
thf(2276,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
thf(2219,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__idem) ).
thf(1980,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(269,axiom,
class_Lattices_Obounded__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
thf(1538,plain,
class_Lattices_Obounded__lattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__I) ).
thf(2486,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).
thf(1285,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff) ).
thf(1738,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
thf(1934,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I7_J) ).
thf(2500,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI2) ).
thf(2113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Otop @ C )
=> ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).
thf(1141,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Otop @ C )
=> ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiE) ).
thf(1023,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( c_Relation_OId__on @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ ( tc_prod @ B @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ B @ ( tc_prod @ B @ B ) ) @ ( c_Product__Type_OPair @ B @ B ) ) @ ( c_COMBI @ B ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__def) ).
thf(1221,plain,
! [A: $i,B: $i] :
( ( c_Relation_OId__on @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ ( tc_prod @ B @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ B @ ( tc_prod @ B @ B ) ) @ ( c_Product__Type_OPair @ B @ B ) ) @ ( c_COMBI @ B ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ C @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(2357,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ C @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D ) @ C ) @ ( c_COMBK @ D @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__const) ).
thf(1427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D ) @ C ) @ ( c_COMBK @ D @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower1) ).
thf(727,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(305,axiom,
class_Orderings_Otop @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
thf(1670,plain,
class_Orderings_Otop @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(612,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) )
& ( ( A = B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP1__E) ).
thf(2584,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1I) ).
thf(1240,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert) ).
thf(2056,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(224,axiom,
class_Lattices_Obounded__lattice__top @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
thf(1358,plain,
class_Lattices_Obounded__lattice__top @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
thf(2247,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD2) ).
thf(2320,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OImage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__empty) ).
thf(1052,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OImage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__rtrancl) ).
thf(1372,plain,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ORange @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__range) ).
thf(595,plain,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ORange @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,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(627,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequiv @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Relation_OImage @ D @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__self) ).
thf(1084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequiv @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Relation_OImage @ D @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_ORangeP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Relation_ORange @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
thf(2479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Predicate_ORangeP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Relation_ORange @ D @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Relation_ORange @ D @ C @ B ) ) )
=> ( c_Predicate_ORangeP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__commute) ).
thf(2088,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__E) ).
thf(2045,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Predicate_Oinv__imagep @ F @ E @ D @ C @ B @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__inv__imagep) ).
thf(2078,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Predicate_Oinv__imagep @ F @ E @ D @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) )
=> ( c_Predicate_Oinv__imagep @ F @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD) ).
thf(1412,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
thf(2325,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__INT__eq) ).
thf(1010,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ C ) )
=> ( ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Int__eq) ).
thf(2226,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ C ) )
=> ( ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_ODomainP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Relation_ODomain @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
thf(1108,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Predicate_ODomainP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Relation_ODomain @ D @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Relation_ODomain @ D @ C @ B ) ) )
=> ( c_Predicate_ODomainP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Otop @ B )
=> ( class_Orderings_Otop @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
thf(963,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Otop @ B )
=> ( class_Orderings_Otop @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Relation_OId__on @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
thf(1062,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Relation_OId__on @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(261,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(1481,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)],[261]) ).
thf(329,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_emptyE) ).
thf(1745,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice @ B )
=> ( class_Lattices_Obounded__lattice__bot @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
thf(2026,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice @ B )
=> ( class_Lattices_Obounded__lattice__bot @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) @ A )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ B @ F ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__subset__iff) ).
thf(2416,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) @ A )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ B @ F ) @ A ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ B @ F ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(588,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right) ).
thf(1253,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) )
<=> ( c_Relation_Orefl__on @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__converse) ).
thf(699,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Orefl__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) )
=> ( c_Relation_Orefl__on @ C @ B @ A ) )
& ( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( c_Relation_Orefl__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
thf(961,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ball__UN) ).
thf(1385,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I6_J) ).
thf(1721,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__Int__distrib) ).
thf(2283,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(258,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
thf(1476,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__iff) ).
thf(896,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(420,axiom,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
thf(2098,plain,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ A )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(1674,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ A )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
thf(1639,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
thf(946,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
thf(1101,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
thf(1558,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( B != A )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D1) ).
thf(2152,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).
thf(1861,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1E) ).
thf(2041,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converse) ).
thf(1777,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(410,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).
thf(2066,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(1706,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ F ) ) @ A ) )
=> ( E = F ) ) )
=> ( c_Relation_Osingle__valued @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedI) ).
thf(2362,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ F ) ) @ A ) )
=> ( E = F ) ) )
=> ( c_Relation_Osingle__valued @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I3_J) ).
thf(1607,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
<=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__iff) ).
thf(1309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) )
& ( ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(536,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclE) ).
thf(1045,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(61,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__empty) ).
thf(716,plain,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ B @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainE) ).
thf(1440,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ B @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
=> ( ( c_Transitive__Closure_Ortrancl @ C @ A )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
thf(2330,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
=> ( ( c_Transitive__Closure_Ortrancl @ C @ A )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).
thf(2095,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Equiv__Relations_Oequiv @ I @ H @ G )
=> ( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( c_Equiv__Relations_Ocongruent2 @ I @ F @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ D @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ E ) )
=> ( c_Equiv__Relations_Ocongruent @ I @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ I ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2__implies__congruent__UN) ).
thf(684,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Equiv__Relations_Oequiv @ I @ H @ G )
=> ( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( c_Equiv__Relations_Ocongruent2 @ I @ F @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ D @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ E ) )
=> ( c_Equiv__Relations_Ocongruent @ I @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ I ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ H ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__I) ).
thf(999,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ H ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert2) ).
thf(1774,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__E) ).
thf(2517,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(382,axiom,
class_Orderings_Oorder @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(1957,plain,
class_Orderings_Oorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Wellfounded_Oacc @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
thf(2385,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Wellfounded_Oacc @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
thf(1395,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).
thf(818,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__constant) ).
thf(1148,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I6_J) ).
thf(2155,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Equiv__Relations_Oequiv @ H @ G @ F )
=> ( ( c_Equiv__Relations_Ocongruent2 @ H @ E @ D @ F @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ G ) )
=> ( c_Equiv__Relations_Ocongruent @ E @ D @ C @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2__implies__congruent) ).
thf(2255,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Equiv__Relations_Oequiv @ H @ G @ F )
=> ( ( c_Equiv__Relations_Ocongruent2 @ H @ E @ D @ F @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ G ) )
=> ( c_Equiv__Relations_Ocongruent @ E @ D @ C @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(81,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
thf(833,plain,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Predicate_Oinv__imagep @ F @ E @ D @ C @ B @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__imagep__def) ).
thf(967,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Predicate_Oinv__imagep @ F @ E @ D @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) )
=> ( c_Predicate_Oinv__imagep @ F @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(950,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ H @ G ) ) @ F ) @ ( c_FuncSet_OPi @ H @ G @ E @ ( c_COMBK @ ( tc_fun @ G @ tc_HOL_Obool ) @ H @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ C ) ) @ B ) @ ( c_FuncSet_OPi @ G @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ H @ C ) ) @ ( c_FuncSet_Ocompose @ H @ G @ C @ E @ B @ F ) ) @ ( c_FuncSet_OPi @ H @ C @ E @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ H @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__compose) ).
thf(2587,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ H @ G ) ) @ F ) @ ( c_FuncSet_OPi @ H @ G @ E @ ( c_COMBK @ ( tc_fun @ G @ tc_HOL_Obool ) @ H @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ C ) ) @ B ) @ ( c_FuncSet_OPi @ G @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ H @ C ) ) @ ( c_FuncSet_Ocompose @ H @ G @ C @ E @ B @ F ) ) @ ( c_FuncSet_OPi @ H @ C @ E @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ H @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_FuncSet_Ocompose @ F @ E @ D @ C @ B @ A )
= ( c_FuncSet_Orestrict @ F @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ D @ F ) @ B ) @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__def) ).
thf(1593,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_FuncSet_Ocompose @ F @ E @ D @ C @ B @ A )
= ( c_FuncSet_Orestrict @ F @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ D @ F ) @ B ) @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__mono) ).
thf(1380,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(396,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(2008,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)],[396]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( c_HOL_Oundefined @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__def) ).
thf(1986,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( c_HOL_Oundefined @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Relation_ORange @ E @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeI) ).
thf(1248,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Relation_ORange @ E @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__iff) ).
thf(2050,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ C @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__Lin) ).
thf(801,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ C @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) ) )
<=> ( ( B != A )
& ( ( A = E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__below) ).
thf(1495,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) ) )
=> ( ( B != A )
& ( ( A = E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) )
& ( ( ( B != A )
& ( ( A = E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(438,axiom,
( c_Arrow__Order__Mirabelle_OProf
= ( c_FuncSet_OPi @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Prof__def) ).
thf(2186,plain,
( c_Arrow__Order__Mirabelle_OProf
= ( c_FuncSet_OPi @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I2_J) ).
thf(664,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__by__empty) ).
thf(1033,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__UN__eq) ).
thf(828,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(532,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__single) ).
thf(1165,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Relation_OId__on @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__onE) ).
thf(1436,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Relation_OId__on @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(358,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice @ B )
=> ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
thf(1859,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice @ B )
=> ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ A )
=> ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ E @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
thf(1693,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ A )
=> ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ E @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__disjoint) ).
thf(2070,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le2) ).
thf(2091,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__empty__right) ).
thf(2404,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__commute) ).
thf(624,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(66,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(740,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)],[66]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__insert__distrib) ).
thf(1352,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Int) ).
thf(2265,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( hAPP @ A @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__upper) ).
thf(1550,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( hAPP @ A @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(365,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(1880,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)],[365]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ F @ C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__ImageI) ).
thf(2484,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ F @ C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I1_J) ).
thf(2372,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Otop @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Orderings_Otop__class_Otop @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__greatest) ).
thf(607,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Otop @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Orderings_Otop__class_Otop @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__inf) ).
thf(2138,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__apply) ).
thf(1320,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(227,axiom,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
thf(1367,plain,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_OPi @ C @ B @ A @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__UNIV) ).
thf(2563,plain,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_OPi @ C @ B @ A @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
thf(543,plain,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ F ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ D @ A ) @ E ) @ F ) @ B ) @ C )
= ( hAPP @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__cut__apply) ).
thf(2059,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ F ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ D @ A ) @ E ) @ F ) @ B ) @ C )
= ( hAPP @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
thf(1037,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Relation_Osingle__valued @ D @ C @ A )
=> ( c_Relation_Osingle__valued @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__subset) ).
thf(1812,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Relation_Osingle__valued @ D @ C @ A )
=> ( c_Relation_Osingle__valued @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
thf(592,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_OaccI) ).
thf(1069,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
<=> ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(659,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
=> ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) ) )
& ( ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I4_J) ).
thf(1565,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__trans) ).
thf(1417,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) ) )
<=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mkbot) ).
thf(972,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) ) )
=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) ) )
& ( ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(2826,plain,
$false,
inference(cvc4,[status(thm)],[892,1823,2336,1767,1899,1315,941,1554,1168,2306,2341,2412,1237,777,555,1818,1295,1211,2512,1596,1290,2062,2014,2099,1443,1808,994,2527,878,655,2380,1971,1533,1078,1671,1756,1735,1999,715,1275,1327,1342,1954,2434,1872,2168,1260,930,2360,1095,2216,2348,1576,709,841,885,1650,1359,1724,1803,1904,1887,651,1127,1782,1287,570,1430,719,1907,2444,1323,1455,1832,1132,1055,1409,1660,1298,2274,917,1545,853,1479,1347,770,1741,1115,1568,2158,1641,1362,1875,2533,1922,902,1704,870,1415,1714,1040,2236,646,1978,2073,2017,2291,1020,574,2281,1119,2002,2286,1433,1201,2367,2437,1896,2190,1447,956,1796,1072,1697,1242,1863,1604,546,925,2118,2047,2232,2083,1915,1708,2093,798,1057,1163,2589,2409,894,825,2541,1355,1123,1676,1751,1487,1883,1217,598,693,630,2414,729,916,1602,1968,1178,1951,583,1787,2345,1407,1634,1573,2068,1624,2327,2213,2492,551,1128,1402,2245,1983,2115,1270,948,1794,1375,1856,1587,2509,1878,1138,2268,1397,742,578,697,1089,1234,1762,2515,1683,1329,2323,1461,1584,1937,1810,1214,1644,679,2317,1419,1028,2023,1292,933,686,1075,837,1825,997,2519,2536,2304,2566,1002,1599,779,1530,1539,1456,1382,2387,1231,1552,2243,1060,1050,605,1759,633,1695,1563,558,1732,1814,1086,953,1185,586,1996,2423,662,2121,1135,965,618,2176,1103,1219,2028,689,2524,1278,1906,1146,1754,2260,601,904,1007,1615,2188,2489,875,1535,958,2398,1965,641,936,1865,1332,1092,1765,804,704,1464,1224,540,672,2521,2229,1894,1542,567,1144,737,1690,1571,863,681,2538,2257,1589,1492,2299,880,649,1043,2197,1307,890,1471,858,1821,621,848,1344,2278,758,1339,2314,2129,2343,609,2111,1630,1993,1556,769,943,2252,1171,2439,1926,2350,2171,883,1176,1113,1477,2101,653,2506,2401,1699,636,695,1066,1445,2064,1015,2390,1250,2005,675,531,548,927,2503,812,939,1958,553,2124,2234,2333,1018,712,1025,872,1156,2143,1647,1368,1780,1484,1098,1547,1748,580,855,1743,1400,2407,1267,1711,2569,791,1188,1785,1901,576,1679,1130,907,1790,1716,1452,1637,2276,2219,1980,1538,2486,1285,1738,1934,2500,2113,1141,1023,1221,2357,1427,727,1670,612,2584,1240,2056,1358,2247,2320,1052,1372,595,627,1084,2479,2088,2045,2078,1412,2325,1010,2226,1108,963,1062,1481,1745,2026,2416,588,1253,699,961,1385,1721,2283,1476,896,2098,1674,1639,946,1101,1558,2152,1861,2041,1777,2066,1706,2362,1607,1309,536,1045,716,1440,2330,2095,684,999,1774,2517,1957,2385,1395,818,1148,2155,2255,833,967,950,2587,1593,1380,2008,1986,1248,2050,801,1495,2186,664,1033,828,532,1165,1436,1859,1693,2070,2091,2404,624,740,1352,2265,1550,1880,2484,2372,607,2138,1320,1367,2563,543,2059,1037,1812,592,1069,659,1565,1417,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SCT123+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 15:50:38 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.88/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.92/1.08 % [INFO] Parsing done (244ms).
% 1.92/1.09 % [INFO] Running in sequential loop mode.
% 2.33/1.29 % [INFO] eprover registered as external prover.
% 2.33/1.29 % [INFO] cvc4 registered as external prover.
% 2.33/1.30 % [INFO] Scanning for conjecture ...
% 2.72/1.43 % [INFO] Found a conjecture and 528 axioms. Running axiom selection ...
% 3.44/1.56 % [INFO] Axiom selection finished. Selected 528 axioms (removed 0 axioms).
% 4.72/1.94 % [INFO] Problem is first-order (TPTP FOF).
% 4.72/1.98 % [INFO] Type checking passed.
% 4.94/1.98 % [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 ...
% 24.76/6.94 % External prover 'cvc4' found a proof!
% 24.76/6.94 % [INFO] Killing All external provers ...
% 24.76/6.95 % Time passed: 6427ms (effective reasoning time: 5849ms)
% 24.76/6.95 % 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)>
% 24.76/6.95 % Axioms used in derivation (528): fact_converseI, fact_converse__meet, fact_single__valued__Id__on, fact_insertCI, fact_ImageE, arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice, fact_converse__converse, fact_SUP1__I, fact_Int__insert__left__if1, fact_adm__wf__def, fact_Pi__I, fact_converse__rtrancl__induct2, fact_singleton__iff, fact_Diff__insert__absorb, fact_inf__eq__top__iff, arity_fun__Orderings_Oorder, fact_refl__onD2, fact_Int__lower1, fact_cut__apply, fact_le__inf__iff, fact_accp_Oequations, fact_subset__UNIV, fact_inf2I, fact_compose__Id, fact_insert__iff, fact_INT__extend__simps_I2_J, fact_IIA__def, fact_xt1_I4_J, fact_unanimity__def, fact_restrictI, fact_conversep_Oequations, fact_inf__sup__aci_I4_J, fact_Image__Int__eq, fact_inf_Oassoc, fact_cut__def, fact_SUP1__iff, fact_rtranclD, fact_bot__apply, fact_UNION__empty__conv_I1_J, fact_INF1__iff, fact_converse__UNION, fact_Transitive__Closure_Otrancl__into__trancl, fact_insertI1, fact_extensional__empty, fact_Int__UNIV__right, fact_UNIV__not__empty, fact_Pi__I_H, fact_Id__compose, fact_INT__D, fact_in__mktop, fact_inf__absorb1, fact_Pi__anti__mono, fact_acc_Osimps, fact_equiv__class__eq, arity_HOL__Obool__Orderings_Opreorder, fact_extensionalityI, fact_in__mkbot, fact_Int__left__commute, fact_order__eq__refl, fact_Range__rtrancl, arity_fun__Lattices_Olattice, fact_rtrancl_Ortrancl__refl, fact_SUP2__E, fact_conversep__noteq, fact_empty__not__insert, fact_UN__extend__simps_I5_J, fact_r__into__trancl_H, fact_Int__UN__distrib, fact_tranclD2, fact_Image__UN, fact_in__inv__imagep, fact_SUP__UN__eq2, fact_INT__subset__iff, fact_INF__commute, help_c__COMBC__1, fact_inf__sup__ord_I2_J, help_c__fequal__2, fact_UNION__empty__conv_I2_J, fact_Image__eq__UN, fact_below__Lin, fact_converse__rtrancl__induct, fact_INT__E, fact_pred__equals__eq2, fact_rtrancl__mono, fact_rtrancl__subset__rtrancl, fact_insert__not__empty, fact_converse__rtranclE2, fact_extensional__funcset__def, fact_bot__fun__def, fact_Diff__subset, fact_acyclic__converse, fact_acc_OaccI, fact_equalityD2, fact_inf_Oleft__commute, fact_rtrancl__converse, fact_Int__insert__right, fact_Range__empty, fact_rev__ImageI, fact_linear__alt, fact_inf1D2, fact_inf__fun__def, fact_INT__simps_I3_J, fact_converse__Int, fact_SUPR__apply, fact_bot__empty__eq, fact_conversep_Ointros, fact_INT__I, fact_inf2D1, fact_singleton__inject, fact_le__funD, fact_emptyE, fact_le__fun__def, fact_acc__subset, fact_DiffD2, fact_Int__empty__left, fact_UN__simps_I1_J, fact_Diff__idemp, fact_Pi__mem, fact_extensional__funcset__mem, arity_HOL__Obool__Orderings_Otop, help_c__COMBI__1, fact_fun__upd__same, fact_inf__Int__eq, fact_extensional__funcset__arb, fact_in__mono, fact_extensional__funcset__fun__upd__extends__rangeI, fact_top__apply, help_c__COMBS__1, fact_Int__absorb2, fact_inf__top__left, fact_UN__extend__simps_I1_J, fact_Int__Diff, fact_DiffE, arity_fun__Lattices_Osemilattice__inf, fact_Domain__empty__iff, fact_INF__INT__eq, fact_mkbot__Lin, arity_HOL__Obool__Lattices_Olattice, fact_extensional__funcset__fun__upd__restricts__rangeI, fact_INT__simps_I1_J, fact_rtrancl__subset, fact_inf__top__right, fact_single__valued__subset, fact_Int__assoc, fact_INF__leI, fact_funcset__mem, fact_top1I, fact_congruent2__implies__congruent, fact_minus__apply, fact_Id__on__iff, fact_Diff__insert, fact_tfl__cut__apply, fact_converseE, fact_fold__graph_H_Oequations_I1_J, fact_order__antisym, fact_refl__onD, fact_fun__upd__idem, fact_trancl__converse, fact_converse__inv__image, fact_inf__commute, fact_UNIV__I, fact_Int__insert__left, fact_Domain__insert, arity_fun__Complete__Lattice_Ocomplete__lattice, fact_acc__downwards, fact_dictator__def, fact_inf1I, fact_inf_Oidem, fact_Domain__mono, fact_INF__INT__eq2, fact_INT__iff, help_c__fNot__1, fact_order__refl, fact_extensional__funcset__empty__domain, fact_SUP1__E, fact_Int__insert__right__if0, fact_xt1_I5_J, fact_insert__code, fact_Diff__triv, fact_UN__extend__simps_I6_J, fact_Domain__empty, fact_inf2E, fact_fun__upd__other, fact_bot__least, fact_UN__extend__simps_I9_J, fact_insert__Diff__single, fact_le__infI2, fact_refl__on__empty, fact_adm__lemma, fact_Image__Id__on, fact_RangeI, arity_HOL__Obool__Groups_Ominus, fact_INF2__D, fact_extensional__funcset__extend__domainI, fact_UN__simps_I9_J, fact_compose__extensional, fact_predicate1D, fact_DomainI, fact_inf__sup__ord_I1_J, fact_inf1E, fact_inf__left__commute, fact_Diff__empty, fact_ex__in__conv, fact_eq__mem, fact_inf__left__idem, fact_notin__Lin__iff, fact_xt1_I3_J, fact_refl__on__INTER, fact_Pi__cong, fact_Pi__empty, arity_HOL__Obool__Orderings_Oord, fact_RangeE, fact_insert__absorb2, fact_UN__I, fact_compose__assoc, fact_equals0D, fact_rtrancl__converseI, fact_inf__bot__right, fact_Id__onE, fact_Image__INT__eq, fact_fun__upd__apply, fact_converse__rtranclE, fact_insertI2, fact_Diff__cancel, fact_insert__absorb, fact_INT__insert__distrib, fact_same__fstI, fact_UN__simps_I4_J, fact_le__INF__iff, fact_trancl__trans, fact_equalityD1, fact_converse__rtrancl__into__rtrancl, fact_Diff__Int__distrib2, fact_inf2D2, fact_Id__on__def, fact_extensional__arb, fact_eqset__imp__iff, fact_trancl__empty, fact_le__funE, fact_INT__constant, fact_DiffD1, arity_fun__Orderings_Opreorder, fact_rtrancl__trans, fact_less__by__empty, fact_irrefl__def, help_c__fequal__1, fact_in__above, fact_insert__inter__insert, fact_Int__lower2, fact_insert__commute, fact_fun__upd__triv, fact_Diff__Int2, fact_extensional__funcset__restrict__domain, fact_trancl__converseD, fact_DomainP__Domain__eq, fact_in__below, fact_Int__absorb, fact_extensional__restrict, fact_Int__UN__distrib2, fact_ord__le__eq__trans, fact_le__infE, fact_INT__extend__simps_I1_J, fact_all__not__in__conv, fact_eq__equiv__class__iff, fact_set__mp, fact_DomainP_Ointros, fact_funcset__compose, fact_mktop__Lin, fact_Diff__mono, fact_UN__UN__flatten, fact_r__r__into__trancl, fact_extensional__funcset__empty__range, fact_eq__equiv__class__iff2, fact_Range__Id__on, fact_subset__equiv__class, fact_total__on__def, fact_accp__downward, fact_Image__singleton__iff, fact_UN__insert__distrib, fact_fun__upd__idem__iff, fact_le__iff__inf, fact_fold__graph_H_Ointros_I1_J, fact_inf_Ocommute, fact_UN__constant, fact_Range__iff, fact_set__eq__subset, fact_rtrancl__into__trancl2, fact_acyclic__insert, fact_Nitpick_Orefl_H__def, fact_SUP__le__iff, fact_equiv__class__nondisjoint, fact_pred__subset__eq, fact_double__diff, fact_inf__greatest, fact_Image__empty, fact_INT__Int__distrib, fact_ext, fact_inf__le1, help_c__fNot__2, fact_inf1D1, fact_UN__simps_I5_J, fact_INTER__UNIV__conv_I1_J, fact_RangeP_Ointros, arity_HOL__Obool__Orderings_Oorder, fact_fold__graph_H_Ointros_I2_J, arity_fun__Orderings_Oord, fact_equalityI, fact_subset__refl, fact_conversep__iff, fact_inf__Int__eq2, fact_equiv__class__eq__iff, arity_fun__Orderings_Obot, fact_empty__iff, fact_single__valued__confluent, fact_le__infI, fact_INT__simps_I5_J, fact_Prof__def, fact_RangeP__Range__eq, fact_inf__apply, fact_converse__iff, fact_Id__on__eqI, arity_HOL__Obool__Lattices_Obounded__lattice__top, fact_INF2__E, fact_fun__upd__upd, fact_Int__commute, fact_PiE, fact_rtrancl__induct2, fact_rtrancl__trancl__absorb, fact_compose__def, fact_linorder__le__cases, fact_UN__empty2, fact_inf__mono, fact_trancl__range, fact_Pi__UNIV, fact_UN__extend__simps_I7_J, fact_acyclic__def, fact_INT__simps_I9_J, fact_trancl__into__rtrancl, fact_ball__UN, fact_refl__onD1, fact_total__on__empty, fact_insert__ident, fact_congruent2__implies__congruent__UN, fact_Diff__disjoint, arity_fun__Orderings_Otop, fact_conversep__eq, fact_SUP__UN__eq, fact_subset__empty, fact_singletonE, fact_IntD2, fact_rtrancl__eq__or__trancl, help_c__COMBB__1, fact_INT__extend__simps_I4_J, fact_Pi__eq__empty, fact_acyclic__subset, fact_INT__extend__simps_I3_J, arity_HOL__Obool__Lattices_Obounded__lattice__bot, fact_extensional__subset, fact_Domain__rtrancl, fact_trancl_Or__into__trancl, fact_funcset__id, fact_tranclD, fact_Domain__iff, fact_converse__INTER, fact_eq__mem__trans, fact_Int__mono, fact_acc__downwards__aux, fact_rtrancl__induct, fact_RangeP_Oequations, fact_trancl__converseI, fact_set__rev__mp, fact_converse__in__Lin, fact_DiffI, fact_inf__absorb2, fact_converseD, fact_Range__def, fact_converse__Id__on, fact_UN__upper, fact_trancl__into__trancl2, fact_Int__insert__right__if1, fact_Diff__Int__distrib, fact_trancl__rtrancl__absorb, arity_HOL__Obool__Lattices_Osemilattice__inf, fact_INF1__D, fact_linorder__linear, fact_DomainE, fact_xt1_I6_J, fact_single__valuedI, fact_Diff__UNIV, fact_INT__empty, fact_single__valued__def, fact_SUP2__iff, fact_accp_Osimps, fact_UN__iff, fact_bot2E, fact_Int__absorb1, fact_rev__predicate1D, fact_insert__Diff, fact_in__lex__prod, fact_restrict__apply, fact_inv__imagep__def, fact_inf__sup__aci_I3_J, fact_inf_Oleft__idem, fact_UN__E, fact_refl__on__Int, fact_Domain__Id__on, fact_cuts__eq, fact_UN__simps_I7_J, fact_equalityE, fact_restrict__in__funcset, fact_in__rel__def, fact_fun__diff__def, fact_INF1__E, fact_congruent2D, fact_INT__absorb, fact_order__eq__iff, fact_congruentD, fact_INF__subset, fact_inf__assoc, fact_rtrancl_Ortrancl__into__rtrancl, fact_rtranclE, fact_Lin__irrefl, fact_refl__on__converse, fact_Int__insert__left__if0, fact_empty__subsetI, fact_insert__Diff__if, fact_UN__equiv__class, fact_accp__acc__eq, fact_bot__empty__eq2, fact_INF2__I, fact_fun__upd__def, fact_Domain__converse, fact_inf__le2, arity_fun__Lattices_Obounded__lattice__top, arity_fun__Groups_Ominus, help_c__COMBK__1, fact_equalityCE, fact_r__into__rtrancl, fact_Int__UNIV__left, fact_fun__upd__twist, fact_conversep__conversep, fact_rtrancl__into__trancl1, fact_Not__Domain__rtrancl, fact_rtrancl__idemp, fact_Diff__insert2, fact_UN__singleton, fact_eq__equiv__class, fact_above__Lin, fact_funcsetI, fact_total__on__converse, fact_conversep__converse__eq, fact_restrict__def, fact_IntI, fact_irrefl__tranclI, fact_subsetD, fact_top__greatest, fact_INFI__apply, fact_trancl__rtrancl__trancl, fact_Id__on__empty, fact_Int__empty__right, fact_dictatorI, fact_in__inv__image, fact_the__elem__eq, fact_insertE, fact_empty__Diff, fact_conversepD, fact_acc__downward, fact_Range__empty__iff, arity_fun__Lattices_Obounded__lattice__bot, fact_Range__insert, fact_order__antisym__conv, fact_eqelem__imp__iff, fact_Diff__iff, fact_INT__simps_I2_J, fact_Int__greatest, fact_subset__trans, fact_IntE, arity_HOL__Obool__Orderings_Obot, fact_pred__equals__eq, fact_Image__iff, fact_UN__extend__simps_I4_J, fact_INT__simps_I4_J, fact_inf__sup__aci_I2_J, fact_Int__left__absorb, fact_Range__converse, fact_SUP2__I, fact_le__infI1, fact_IntD1, fact_iso__tuple__UNIV__I, fact_INT__insert, fact_compose__eq, conj_0, fact_INT__extend__simps_I9_J, fact_SUP__commute, fact_Int__iff, fact_mem__def, fact_UN__simps_I6_J, fact_refl__on__Id__on, fact_UN__equiv__class2, fact_Image__INT__subset, fact_inf__idem, fact_INF1__I, fact_INTER__UNIV__conv_I2_J, fact_refl__rtrancl, fact_UN__subset__iff, fact_equiv__class__self, fact_Image__mono, fact_rtrancl__trancl__trancl, fact_inf__sup__aci_I1_J, fact_rtrancl__converseD, fact_INT__extend__simps_I5_J, fact_inf__bot__left, fact_ord__eq__le__trans, fact_fold__graph_H_Oequations_I2_J, fact_INF__const, fact_not__acc__down, fact_doubleton__eq__iff, fact_insert__Diff1, fact_order__trans, fact_SUP__const, arity_HOL__Obool__Lattices_Obounded__lattice, fact_SUP__subset, fact_INF2__iff, fact_disjoint__iff__not__equal, fact_restrict__extensional, fact_trancl__domain, fact_single__valuedD, arity_fun__Lattices_Obounded__lattice
% 24.76/6.95 % No. of inferences in proof: 1060
% 24.76/6.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6427 ms resp. 5849 ms w/o parsing
% 25.42/7.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.42/7.28 % [INFO] Killing All external provers ...
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